I think it is highly unlikely. The bank would be increasing their exposure on your loan, there is no equity to lend on. The time to try this was when you were buying, too late now I now but at that stage you could have applied for a percentage of the new value with extension completed so your purchase price as such would be the actual purchase price plus cost of renovations. This is how this would normally be treated.
In an existing mortgage situation usually top up mortgages are limited to 80% of value of property, this was the case even in the good old days, as you are already well past that it doesn't leave you any scope. Unless there is some system in place with your lender to facilitate negative equity cases I don't see this being easy if even possible.