Jaitesh - to 'add yourself' you would need the surviving joint owner to transfer the whole legal title/ownership to herself plus you. So you would need 'signed paperwork' I'm afraid.
You refer to TIC and I assume that the trust arrangement has been protected on the register by way of a form A restriction
See
Joint property ownership: Overview - GOV.UK
If so then the trust and your beneficial share/interest is protected albeit you are not named on the register. If you are concerned with regards what your legal rights are and indeed how the surviving owner is 'restricted' then please do seek legal advice