What's the average price difference between LH / FH in the UK ?
Asked another way - what discount can one factor in when buying a LH
as opposed to a FH ?

An 'average' is pretty meaningless because some types of property,
such as flats, are usually leasehold (or commonhold) and others (such
as houses) are predominantly freehold, so there is no direct
comparison.

The value of a leasehold property varies according to the length of
the lease (sometimes as long as 999 years, but often only 100 years).
Critically you must pay the freeholder to extend your lease if the
time left on it dwindles to a point that makes it difficult to sell
(generally thought to be 60 years or less).
http://msn.whatmortgageonline.co.uk/holding.htm

Buying a leasehold property is often not much cheaper than buying a
freehold. This may seem a bit bizarre seeing as you don't actually own
anything - you pay out a huge single lump sum to take possession of
the space within the building. OK, so you can renovate, redesign and
refurbish (as long as it is within the terms of the lease), but if the
lease were to expire tomorrow, you'd probably have to leave all the
fixtures behind.

The difference in market value between a freehold property and a
leasehold property is slight Few people nowadays retain a lease until
it expires and it's increasingly easy to extend the lease anyway. The
cost of the lease reflects current property values and it's quite
likely you will be able to buy a leasehold property and sell it a few
years later at a profit, even though it has less time to run on the
lease.
http://www.themovechannel.com/howto/find/leasehold-costs.asp

Please note that your question relates primarily to English law (not
UK). Scotland has used a completely different (predominantly feudal)
property law.

Owain

Just one small point to add to owain's comprehensive commnent. As
owain says, most flats (apartments) in England are leasehold, but
there are some houses converted into flats, where the residents in the
separate flats share the freehold. Building societies and banks can be
reluctant to lend money to purchase such flats, because it is
sometimes unclear from the Deeds just who has responsibility for
maintaining and repairing the exterior and common parts of the house.
Such a freehold flat can therefore be worth less than an equivalent
flat with a regular lease.

It is unlikely that a flat or apartment would be totally 'freehold'
- unlikely - but not impossible - however very, very, unlikely

Assuming you are interested in freestanding properties, then the price
differential depends on the length of the lease and the covenants
(which can be evil)

Probably the easiest way of estimating it is the cash buyout sum that
was introduced some years ago - which is compensation for loss of
ground rent.
That is pretty simple - GBP 1000 pa is worth 20,000 at 5%

If you are looking at flats, then perhaps rephrase the question.