National Savings and Investments (NS&I) has increased the returns on some of its accounts, with many now paying more than 5% for the first time in nearly three years.

Competition in the savings market has been growing, leading to some of the highest interest rates for years.

However, in the current climate, attractive deals do not always hang around for long, says Rachel Springall at the financial data website Moneyfactscompare.co.uk. If a provider attracts enough savings cash it will pull a product from sale.

NS&I has upped the rates on its “British savings bonds”, which are rebadged versions of its guaranteed growth bonds and guaranteed income bonds. They offer a fixed interest rate over their one-, two-, three- or five-year bonds.

The deals are available to new customers and those with existing accounts that are maturing. With the growth version, interest is added each year and paid when the bond matures, while with the income version, interest is paid monthly.

Looking at the growth bonds, the new interest rate on the one-year product is 4.99% (up from 4.82%), while the two-year rate has risen to 5.07% (was 4.81%). The three-year rate has gone up from 4.83% to 5.1%, while the five-year rate has been increased to 5.17% (was 4.85%).

Those are pretty competitive rates, though as Sarah Coles, the head of personal finance at the advice firm AJ Bell, says, “you can still make more money elsewhere”.

At the time of writing, the top-paying one-year fixed-rate bond was paying 5.12%, while the highest-paying five-year fixed bond was offering 5.37%. But getting the very highest rates sometimes means signing up with less-well-known names. The one-year deal is from Union Bank of India (UK), while the five-year version hails from GB Bank.

If you have a very large sum that you need to stash somewhere – for example, the proceeds of a house sale or an inheritance – these NS&I bonds have one big thing in their favour: you can invest up to £1m per person in each bond issue. The minimum investment is £500.

As NS&I says, “most banks only guarantee your savings up to £120,000,” whereas it is backed by the Treasury and is “the only provider that secures 100% of your savings above this amount”.

Also, it means you are putting your money into the government’s savings bank, and “your savings will be invested back into supporting the UK”.

Money invested in NS&I’s British savings bonds cannot be withdrawn before the end of the fixed term.

That will not suit everyone, and it is a good idea to keep some money in a high-paying easy access account to cover things such as unexpected bills. Earlier this month the digital bank Starling announced that people who sign up for its Easy Saver account will enjoy a table-topping 5% interest rate. This account offers unlimited penalty-free withdrawals, but that rate (made up of a 2.5% variable standard rate, plus a 2.5% fixed interest bonus lasting for six months) only applies to those who open, or have opened, a Starling current account on or after 1 October. The rate applies on balances of up to £25,000.

Starling customers who signed up before then can benefit from a 4% rate when opening a new Easy Saver. That includes a 1.5% fixed interest bonus for six months.

Meanwhile, the savings provider Marcus by Goldman Sachs this week upped the interest rate on its one-year fixed-rate savings account from 4.3% to 4.75%.