I suggest a full analysis of income should be carried out to ensure that the taxable, exempt and non-business income is properly classified and you review which PE method suits you.
When that data has been evaluated, an accurate assessment can be made as to whether the floor space method or an alternative partial exemption special method is suitable.
The floor space method works by considering how much floor space is used in making taxable supplies compared to the total floor space used for making taxable and exempt supplies. The floor space given over to common areas such as cloakrooms, toilets, staff rooms, office areas and corridors etc. is excluded from the calculation.
I agree HMRC have historically been opposed to methods based on floor space. There are a number of cases in which the taxpayer has been unsuccessful including e.g. Vision Express (UK) Ltd  and Aspinalls Club Ltd (LON/99/540 .
However, a more recent case involving London Clubs Management Limited (“LCM”)  EWCA Civ 1323 held that a floor space method was acceptable for that particular casino. LCM was successful in the First and Upper Tier Tax Tribunals, as well as the Court of Appeal. Whilst that is encouraging, it must be noted that judgment specially mentioned that the case was fact specific to the taxpayer involved. It cannot therefore, automatically be assumed that what was acceptable for LCM will be suitable for you.
Its also worth noting that changing the PE method to some special method takes ages and HMRC requires a lot of supporting documentation to support your assertions.
Hence all this should be reviewed – looking to the cost vs benefit of the change.