Is this a clutch problem?

Not being technical minded on cars, if I accelerate hard whilst over-taking or drop a gear going up a steep hill the engine sometimes over-revs, but the car does not go any faster. If I lift off things seem ok. Otherwise she runs fine and is very reliable. This is a high miler.

The clutch is slipping and needs replacing - this will rapidly get worse so needs fixing asap.

I agree.