There's still one
There are 2 distinct and separate issues: VAT deductibility and loss of PPR relief from CGT.
A deduction can be claimed for VAT charged in respect of goods/services supplied in so far as they are used for the purposes of making taxable supplies. There's no provision of which I am aware which restricts goods/serivces to be used in or on property owned by the taxable person.
So in theory a deduction could be claimed in the circumstances set out by OP.
PPR relief may be lost if the part of the premises is used
exclusively for business purposes. This means that if it is used part business/part personal then there shouldn't be any loss of PPR relief on disposal.
Where the VAT deductibility and PPR relief could interact is if full deduction for VAT incurred on improvements to the premises was claimed, it would be one indication that that part of the premises was used exclusively for business. As the expenditure was incurred by the company it couldn't then be claimed as enhancement expenditure when calculating CGT.
The alternative would be to claim VAT incurred in proportion to business use, which would help demonstrate that there is a non-business element to the use of the premises. Of course, all facts would need to be considered to conclude one way or the other.
In my opinion, it's just not worth it.