Government figures released in response to a freedom of information request by Hargreaves Lansdown showed about two million people will get less than the £148.40 a week new state pension, outlined by the government, in its first five years.

Hargreaves said the majority of people falling short of the full state pension are likely to have been contracted out during their working lives. Other people who get less than 100 per cent are likely to have interrupted National Insurance contribution histories, such as mothers or the self-employed.

The firm added the formula for calculating the new state pension entitlement “is complicated”.

For those who have been contracted out of the second tier state pension it involves making a deduction from their state pension entitlement to reflect the fact that they have been able to build up a larger private pension using the National Insurance rebate.

The flat rate state pension will be effective from April 2016. It aims to simplify the current two-tier system.

However, Hargreaves Lansdown found only 45 per cent of those retiring in the first five years from April will receive the full state pension and one million will receive less than 86 per cent.

Head of pensions research Tom McPhail (pictured) said: “The new state pension will ultimately be a simpler and fairer system. However in the short term it will be complicated and many people are likely to get less than they may expect.

“With the new pension freedoms meaning that they will be free to spend all their private pension savings, it is imperative that they receive a proper state pension forecast. Without this, they could get a nasty shock when they do reach state pension age.”