Hi Rachel - we don't register 'homes'. We register land and a single property can comprise more than one registered parcel of land for example.
I think your post is really aimed at something other than an amalgamation though
You have one registered title and within that title there are two separate 'homes' and addresses. Your intention is to combine them into one 'home' and one address.
If so then you need to contact the local authority street name & numbering department to arrange for the change of postal address. They will confirm what single postal address is to be used.
Once you have that you can apply to update the current register to refer to the single postal address as follows
A registered proprietor or their conveyancer can write to us or complete form AP1 to change the property description. For example, to change the property's name.
You need to send us evidence from the street naming and numbering department of the Local Authority. Royal Mail documents are not acceptable as their delivery point address description can differ from the Local Authority registered address.
When submitting your application, please remember to tell us the address you would like a copy of the updated register to be posted to upon completion, as this can often be different from the property itself.
There is no fee for this application
Where to send your application
HM Land Registry address for applications.