This is good news, but a note of caution. Reading the Deregulation Bill I don't think it grants direct access to the registers, nor does it create any immediate additional right to obtain information from them. For births and deaths it adds to the relevant acts (amongst other provisions):
...
(1) The Minister may make regulations for the purpose of enabling the Registrar General-
(a) to carry out, on request, a search to find out whether the Registrar General's certified copies contain a particular entry;
(b) to provide, on request, a record of information contained in an entry in the Registrar General's certified copies, otherwise than in the form of a certified copy.
(2) The regulations may authorise or require the Registrar General to charge a fee of an amount specified in the regulations for carrying out a search or providing a record.
...
In other words, there is no immediate change at midnight. All that has become legal is for the Minister at some future point to publish some regulations increasing access. The bill doesn't stipulate that the Minister should do this - it merely becomes lawful for him or her to do so. If such regulations are made, that access will be in the form of a new search service for which there will be a charge, from which the results will be given in a form other than the traditional certificates.
For marriages and civil partnerships the bar is set slightly higher - it has to be the Secretary of State rather than the Minister who makes the regulations, the regulations have to be a statutory instrument, and they can only be prepared after consultation with the Registrar General.
Therefore whilst this is a step in the right direction it isn't necessarily going to be quick, and it won't be free (I do hope they don't make it £9.25!)
Richard.