I understand that anyone can pay £2,880 a year into a pension and receive tax relief from the government boosting it to £3,600, even if they are not a taxpayer.
If this is the case, why wouldn’t someone pay £2,880 into a pension one year, then withdraw a £3,600 small-pot cash lump sum the following year, then reinvest £2,880 in a new pot? This seems an easy way to get £720 a year indefinitely.
Yes, in theory you can do this, but you should be aware that the whole area of pension recycling is one that the government is looking at carefully.
For instance, in April 2015 the Money Purchase Annual Allowance (MPAA) was introduced, which limits the amount that can be contributed to a pension once it has been accessed flexibly. This MPAA was initially set at £10,000, but in 2017 it was reduced to £4,000. While that is still above the £2,880 you refer to, it is clear that this is an area the government is willing to take action on if it feels it is being abused.
A steady record of contributing £2,880 a year and then withdrawing £3,600 would be enough to get alarm bells ringing for both pension providers and HMRC.