It depends. As the person you bought the car off isnt in the business of selling cars you are at an automatic disadvantage vis a vis consumer law protection.
There is however an implied condition under s13 Sale of Goods Supply of Services Act 1980 that the sale of a car (whether privately or otherwise), that at the time of delivery, it is free from any defect which renders it a danger to you or others. Now bearing in mind you bought the car in Oct and it's now March is an issue...it really boils down to the facts and circumstances.
You need professional advice including a mechanic's opinion to give you a definite answer. Factor in the cost/inconvenience V value of car and come to a decision.
On the face of it it seems improbable you have any comeback.