In my experience, HMRC will issue the refund within a month or so, although in certain cases where a known claims firm is involved with a history of making dodgy refund claims, they may withhold any refund while they enquire into the claim.
Even if HMRC pay the refund promptly, they will often then open an enquiry into the refund claim to check that the facts meet the conditions for the relief claimed. If following their enquiry, they decide that the refund should not have been made, they will issue a closure notice requiring repayment of the tax claimed. This decision can, where appropriate, be appealed to the tax tribunal.