The action group that claims investors were misled by Royal Bank of Scotland over its £12 billion rights issue in 2008 has urged its members to accept the terms on offer from the state-owned bank.

The RBS Shareholders Action Group’s letter, sent out last night, says that “having carefully considered the merits of the current offer” it has decided to accept the 82p-per-share offered by RBS. The action, which has cost RBS £129 million, could end this week.

The case will return to the High Court on Thursday, when Mr Justice Hildyard will hear if it is to proceed. The group represents about 9,000 private investors.

The letter makes clear that while the 82p offer is below the 92p that the investors have been holding out for, “there are a number of practical and legal risks which had to be considered”.

One is the possibility that even if the shareholders are successful, RBS could appeal, driving up costs.

There would have to be a further trial to assess the level of damages, with no guarantee that these would match the 82p on offer.

The letter says that the claim is being funded by a “substantial claimant”, a reference to Trevor Hemmings, the leisure magnate, and that he has decided to accept and is no longer willing to fund the action.

Mr Hemmings could not be reached for comment, but reports suggest he has decided to accept the terms. Royal Bank of Scotland refused to comment.

The case is also being brought by various institutional shareholders in the state-controlled bank. The action group claims they too have accepted the 82p on offer.