My Mrs has recently bought a Mk7 Golf 1.6 TDi. The car itself drives well with no issues and she is happy with it but I noticed the other evening that, after shutting the engine down, the cooling fan is on for what seems like a long time.

Means the DPF is carrying out a regen. For the long term reliability of the system its best to continue driving until the regen is complete.

My previous car (Mk6 Golf 2.0 TDi) did the same thing. Never noticed it doing a regeneration while driving, only noticed after switching the engine off when the fan kept running, while producing a characteristic smell of oil/diesel & hot rubber. Sometimes it would happen twice in one week, other times it would go several weeks without it happening.

Never understood why they don't have an indication on the dash to let you know a regeneration is running so you can decide whether to keep driving in order that it completes the process.