I agree with M0nica.
It is fairly simple to contact the Land Registry, and change the entry to joint names, but you do need to decide whether you are tenants in common (both of you own all the house together and either inherits on the death of the other) or joint tenants (each of you owns half the house and you can do what you like with your own half)
There is more about this on gov.uk, and it makes sense to read it and think about it before going to a solicitor.
It also makes sense to make wills anyway, and if either of you have children from the first marriage, you need to think about inheritance issues.