Recovering costs for solicitors fees without going to court in the UK?

IM in a legal dispute with another person over contested probate in the UK. I have initiated this legal action and it has cost me a fair amount in legal fees. IM hoping the issue can be settled without going to court and if this happens where do I stand regarding recovering legal fees?. Can I recover any of my solicitors fees from the other party if a settlement is agreed out of court?