It's a known issue with the THP. If the car was serviced always at Peugeot, following their requiriments/periods, you should be able to get at least some help with the bill.
As you bought the car just 2 months ago, you're covered in case you've bought it from a dealer, being it a Peugeot or not. 6 months as, I can bet my life on it, that the engine was developing the problem way before you get it.
If somehow you need to pay for it yourself, any peugeot, citroen or mini specialist would be able to do it, as they've models using the THP.
First step, back to the seller. Always give the chance to repair it. If they fight back, get it done, and sue in Small Claims for the cost of repairs. Always comunicate using a valid prrof, as Royal Mail Special Delivery mail.
Worth doing at the same time, if wasn't done before, the water pump, as despite the low milage, should be done every 4 or 5 years. That would be paid by you, but totally worth.