Oil In the Coolant

I think I may have found the culprit, one the lines going into the radiator has a leak. does the radiator need changing or it is just changing the lines?

A leaking internal trans cooler inside the radiator could allow transmission fluid into the coolant. Since you're in the UK and I'm not sure which powertrain you have and if it's applicable, if your car has an oil-to-coolant heat exchanger those can also leak internally and allow oil and coolant to mix.

A cracked turbocharger CHRA (center housing rotating assembly) for a water and oil cooled turbo could theoretically allow coolant into the engine oil, but since the housing isn't pressurized with oil outside the bearing surfaces (and in fact would leak oil past the dynamic seals into the compressor and turbine wheels if the CHRA were pressurized with oil), you wouldn't see oil getting into the coolant from a turbo problem.

Other most common source for oil getting into coolant system would be a head gasket leak, but with modern multi-layer steel head gaskets they usually don't weep oil to coolant passages and vice versa but instead normally fail catastrophically. It would still be a possible source if you have a trans cooler in the radiator or oil-to-coolant heat exchanger you've ruled out.

Another test you could do is to send a sample of the engine oil in to an independent testing lab for a used oil analysis. In the US there's companies like Blackstone Labs and others that can do an analysis of the motor oil and this will often show if even tiny amounts of coolant is getting into the engine oil well before it becomes a milky sludge. I'm not sure if any of the testing labs might be able to take a sample of the coolant and identify what type of oil (ATF, motor oil, etc.) is present.