Forms for recognising joint ownership in equity on register

Hi
My partner and I have owned registered property since purchase with equal contributions to purchase price. However when it was bought I was registered in one sole name. We want the legal title to reflect the equitable ownership, which is 50:50 tenants in common. We do not have a formal trust deed but could have one drawn up.
You will see the property is not being sold. There is no consideration. We come up with different answers when asking which forms we need to complete and fees. The property is mortgage free and not subject to charges. It is worthcirca 650k Please can someone help. Many thanks in advance.
 

Hi Tony - our online guidance explains what forms you need, namely form AP1 (application form), TR1 (transfer deed) and forms Id1/conveyancer or ID3.others as listed to have your identities verified - Registering land or property with HM Land Registry: Change the registered owner name - GOV.UK
The sole registered legal owner transfers the whole of the legal title to themselves plus partner
The registration fee is payable under Scale 2 of the fee order on half the current market value. It is a postal application only if you are doing this yourselves
Complete panel 4 of form ASP1 to refer to Transfer 1 to 2 - Full value £XK - pay calculated fee
 

Dear Adam
Thank you so much for your help and quick reply. Really appreciated.