Building a one-­million-pound ­investment portfolio by retirement may sound a glorious pipe dream. It couldn’t happen overnight, of course, but with careful planning and regular savings, it is more achievable than you might think.

Savvy investors can put a rocket under their investments if they use the power of dividends by reinvesting them over time – rather than spending them. An investor who had put £500 a month into the UK stock market over the past 40 years would have a £1.4million pot today – but that’s only if they reinvested the­ ­dividends they had received.

Without this it would be worth a less impressive £506,000, according to investment platform Bestinvest.

Current high yields in the UK mean a million-pound pot is possible for those with time on their side, and who pick the right funds to benefit from the magic of compounding. This is the snowball effect that increases the value of portfolios as money is reinvested.

The UK stock market is a happy hunting ground, with some stocks yielding more than 9 per cent, which means a cash payout of £9 a year for every £100 you invest.

These payouts have made up more of the return for UK investors than any share price growth. Jason Hollands, of Bestinvest, says: ‘Where these are reinvested back into shares rather than banked, the effect is particularly powerful.’

So how can you get started today if you want to hit that million-pound mark? Many UK companies that are household names offer dividend payouts which dwarf the returns available from a bank account.

These include insurance ­businesses Legal & General and Phoenix Group, which yield more than 9 per cent. A 9 per cent annual return would give you a million-pound ­portfolio in just 31 years, but ­Hollands cautions against simply picking the stocks with the highest yields now and expecting to become a millionaire over time.

‘It is unwise to select a fund or stock solely based on a high dividend yield, without first ­checking that it’s sufficiently ­covered by profits and that the dividend is not at risk of being cut,’ he says.

Instead, he suggests starting by using funds that invest in high-yielding shares with strong business prospects to build a ­million-pound portfolio. And always ensure you’ve ticked the right boxes to ensure that your dividend helps your money to grow.

Make a plan you can stick to

To set out to become a dividend millionaire is a long-term undertaking. Make sure you’ve set everything up correctly in the first place to give your money the best chance to grow over time.

That means picking an investment platform that gives you access to the funds you’ll be buying and with the lowest charges.

Then, set up a regular payment into your chosen funds and ensure you have ticked the right boxes so dividends are reinvested.

Most platforms allow you to set preferences to automatically ­reinvest any dividends paid from exchange-traded funds, shares, or investment trusts.

If you buy other types of funds, ensure you pick the ‘accumulation’ units rather than the ‘income’ units of the fund. This means income paid out from these will be automatically reinvested.

To avoid dividend tax, levied at 8.75 per cent on any dividends over £500 for basic rate taxpayers – 33.75 per cent for higher rate taxpayers – set up an Isa for your dividend portfolio.

Pick the right funds for secure returns

While buying individual high-yielding FTSE 100 stocks is a tempting way to take advantage of the compounding effect of dividend payments, there’s a danger that the companies behind them will stop paying dividends, and that yields will fall over time.

‘Dividend yields are not fixed and will vary year to year based on the share price as well as actual payouts,’ Hollands warns. If you buy individual high-yield stocks, check that the company is able to pay out its dividends by using a measure known as ‘dividend cover’. This divides the earnings per share by the dividend per share and shows how many times a company could afford to pay its dividend from its profit. A low measure suggests a firm may fall into trouble or cut its dividend later.

Buying a high-yielding fund or series of funds may be a safer way to build your portfolio.

Alex Watts, data and fund analyst at investment platform Interactive Investor, says active managers who focus on dividend-paying firms can ensure these are ‘financially sound and generating enough cash flow to maintain or grow distributions’.

He suggests putting money into Artemis Income, which yields 3.4 per cent, but also concentrates on capital growth. The fund has risen 27 per cent in the past three years as well as paying out cash. ‘Management on the fund has a clear mantra of “cash flow first and dividends second”: in short, they prefer to hold companies that can consistently generate strong cash flows, which is key to fuelling the dividend shareholders receive,’ he says.

Laith Khalaf, senior financial analyst at investment group AJ Bell, suggests buying City of London investment trust, which focuses on dividend growth. The trust yields about 5 per cent annually and has seen 57 consecutive years of dividend increases.

The trust – up 26 per cent in the past three years – has been run by Job Curtis since 1991, and focuses on UK large-cap companies.

Rob Burgeman, senior investment manager at wealth manager Brewin Dolphin, suggests Murray Income, another investment trust. He reckons these trusts, which are stock market-listed and can hold back some profits in good years to pay out in lean times, are attractive for anyone wanting to build a portfolio with dividends.

He says: ‘They hold decent levels of reserves to smooth out the income they provide over difficult periods – there are many considered ‘dividend heroes’, having increased their dividend every year for 50 years or more.’

Murray Income has returned 281 per cent in capital terms over the past 35 years. But, with dividends reinvested it returned 1,498 per cent, Burgeman says.

The trust focuses on large UK firms such as Unilever, AstraZeneca, and RELX.

Use a pension to save faster

Exploiting the power of your pension could get you to millionaire status far more quickly. This is because the Government allows tax relief on any contributions made at your marginal rate of income tax, whether a basic, higher, or additional rate taxpayer.

A £500-a-month contribution into a Sipp attracts £250 of tax relief for those paying tax at 40 per cent. Adding this in, and assuming a 6 per cent annual growth rate, with reinvested dividends, would make you a millionaire in 35 years.

If you could achieve a 9 per cent return – as offered by the current yield on stocks like Phoenix and L&G – you could reach the magic million in under 28 years. Of course, all this depends on no major changes in the next Budget.

Use the power of time to grow wealth

Albert Einstein called compounding ‘the eighth wonder of the world’. And you may find plenty to marvel at in the cumulative power of reinvesting dividends.

Staying the course over decades means you could end up with a huge sum before retirement, with the bulk coming from dividends, rather than share price growth.

Stock market codes

Artemis Income: B2PLJJ3

Murray Income: 0611112

City of London Investment Trust: 0199049