The Land Registry will see that there is a 'charge' in section C of your title deeds & will need the lender's consent. If you had been able to transfer half to your wife without your lender having the chance to be involved it would affect their rights over the property in respect of the mortgage. They have to be involved & it may require a remortgage since a new mortgage offer to both of you will be needed.
Moreover, you and your wife need legal advice on the different implications of whether to hold the property as joint tenants (survivor inherits deceased's share) or tenants in common (deceased can dispose of their share in their will) (see section 10 of TR1).
Best to get a solicitor to do it. It ought not to cost much for a simple remortgage (ask lender if they would dispense with the usual searches - apart from bankruptcy searches which they will want done - check Land registry website for cost of latter).