they cant charge you for a whole new carpet.
what they have to do is find out how much the carpet cost per square meter when it was new. then depreciate ot by the age for wear and tear. then work out how much at this rate it would cost for the actual size of the damaged area, and charge you that.
expecting a whole new carpet at the tenants expense is betterment, and is not allowed.
Its not quite that simple :
"In considering whether cleaning/repair is necessary versus complete replacement at the
end of the tenancy, an adjudicator will examine the check-in/out reports, any statements
of condition and any photos/videos in order to compare the condition of the property at
the start and end of the tenancy. In some cases, the damage may not be so extensive as
to require the complete replacement of an item at the tenant’s expense (such as a kitchen
worktop or carpet); however the adjudicator will award sums in recognition of any damage
which has occurred. Whilst the landlord may wish to replace a damaged item, it is not always
the case, even where the damage is admitted by the tenant, that the extent of the damage is
such that the tenant should automatically bear the full replacement cost.
In the rare circumstances where damage (to the worktop/carpet/mattress/item etc) is so
extensive or severe as to affect the achievable rent level or market quality of the property,
the most appropriate remedy might be replacement and to apportion costs according to the
age and useful lifespan of the item. An example of how this might be calculated is set out
below:
a) Cost of similar replacement carpet/item = £500
b) Actual age of existing carpet/item = 2 years
c) Average useful lifespan of that type of carpet/item = 10 years
d) Residual lifespan of carpet/item calculated as ‘c)’ less ‘b)’ = 8 years
e) Depreciation of value rate calculated as ‘a)’ divided by ‘c)’ = £50 per year
f) Reasonable apportionment cost to tenant calculated as ‘d)’ times ‘e)’ = £400"
Question is would the rip have affected the let potential? Landord has assumed yes, its quite possibly true. However a simple repair may have removde that fact. E.g. A foam backed carpet could have been stuck down, a higher quality carpet could have a repair which would be about £50 from a carpet layer.
Thats of course assuming that the OP GF did the damage which they refute anyways.
Betterment relates to taking an old worn out item and expecting a new for old approach.
If £200 was the new carpet its either cheap initially and replaced with similar, or landlord has gone for a cheaper one anyway.