Getting name on Title Deed for home

[Homecony9]

Afternoon

My husband and son own the house we live in (England) and they also have a substantial mortgage on the property.

I have now sold our previous home which was solely in my name.
I want to pay a substantial sum (equivalent to 50% of the property's value) and want my name included on the property Title Deed.
We could not do this when my husband and son purchased the house as the mortgage lender would not allow my name on the mortgage (apparently they only allow 2 people to be on the mortgage) and my income was the lowest, and we had to act fast to beat the Stamp duty holiday deadline.

So the Title Deed should say I have a 50% share of the equity of the house, my husband will have circa30% and the my son 20%, and the mortgage will be reduced to about 25% of the value of the house.

Question: is this allowed by law, and can the lender object to this arrangement?
How much should it cost in legal fees?
Do we even need a solicitor for this? Can we just fill in a form and sent it to the Land registry?
Anything else to look out for?
Thanks

[dslippy]

There is no mechanism for obliging a third party to propose a sale to you.

[Homecony9]

There is no mechanism for obliging a third party to propose a sale to you.

We all consent to this arrangement, so no issue there.
It's just a case of how to go about it.
I think a TR1 maybe required.

[dslippy]

Sort out the allocation of the property as between yourselves first.

[Homecony9]

PS - Husband and son are currently "Joint Tenants" so I guess this will need to be changed to "tenants in common" first?