On 29th June 2017 the Marriage Registration Bill was introduced. The Bill is sponsored by the Bishop of St Albans. Its text can be read here. It would enable mother’s names to be added to marriage certificates and update the technological processes of registering marriages.
Hansard records the Introduction as:
Registration of Marriage Bill [HL]
A Bill to make provision about the registration of marriages.
The Bill was introduced by the Lord Bishop of Peterborough (on behalf of the Lord Bishop of St Albans), read a first time and ordered to be printed.