Tiger Moth,
A full scale, rib for rib, wire for wire,replica would be prohibitively expensive - it's a big aeroplane, with an awful lot of parts. At a wild guess I'd say £100,000 for the airframe. and you would you find it at all easy to locate an appropriate engine. Yours is not an uncommon desire: what people usually do is build the eminently practical Replica Plans 7/8 scale version and bung in a C-90 or similar.
see
http://www.historicair.com/replicaplans/
Build and running costs should be roughly equivalent to any other single-seat small engine wooden homebuilt biplane e.g. Isaacs Fury (though the Isaacs Fury is what I'd prefer myself). People seem to put these things together for around £20K plus a lot of work. Suggest you enquire at the PFA website.
You often see Isaacs Furies for sale at around £12K to £15K, but as far as I know there is only one Replica Plans SE5a in the UK (wasn't it Mike Beach's)
There's apparently one for sale elsewhere, though: see -
http://www.kcdawnpatrol.org/Forsale.htm.