According to Pooleys 2006 they do with landing fee at £11.21 per tonne or part + VAT - but be careful - it also says handling mandatory for all GA aircraft - and this can often be more than the landing fee. Some airports also have a host of other charges, such as departure fees, security fees, etc. Best bet is call one of their handling agencies, such as Signature, on 0121 782 1999
Hope this helps!
DW