I quote below from the court service website
Her Majesty's Courts Service will meet the reasonable costs of interpreters for deaf and hearing-impaired litigants for hearings in civil and family proceedings.
Many people have a friend or relative who usually interpret for them. If the deaf person wants such a person to interpret for them, they will need to ask for permission from the Judge. The Judge must be satisfied that the friend or relative can exactly interpret what is being said to the court and what the court is saying to the deaf person.
Unless the relative or friend has a recognised qualification in relaying information between deaf and hearing people, it may be better to use a qualified interpreter. The friend or relative may still be able to attend and provide support, but permission should be sought from the Judge first.
If an interpreter is needed, the court will make arrangements for an interpreter to attend.
I quote from the LSC guidance (pdf file) on payments for interpreters for deaf or hearing impaired clients (outside court situations).
In light of preparations for the public duty to promote disability equality to come into force in January 2007, the Commission will now bear both the ‘reasonable and unreasonable’ adjustment costs so that deaf clients are not denied access to language support where appropriately employed and where reasonable in amount.
As well as the cost of English/British Sign Language interpretation we will pay the reasonable cost of other Language Support Professionals (LSP), such as Speech to Text Reporters, Lipspeakers and DeafBlind Manual Communicators, if the engagement of such professionals is reasonable and necessary to communicate effectively with the particular disabled client. Further guidance may be developed on this.
In criminal cases the CPS advises that according to a court authority, the true record of a sign language
See Re S-A  EWHC 2942 for a case in which communication by British Sign Language featured prominently.
The Community Legal Service has a special website with information & legal advice for those who use sign language.
National Register for Communication Professionals Working with Deaf & Deafblind People
British Deaf Association