Do you have to be a licenced airfield to provide radar?
No. It's not connected. Aerodrome licensing is to protect users of Public Transport. The ANO requires that, in the United Kingdom, most flights for the public transport of passengers take place at a licensed aerodrome, or at a Government aerodrome. See
CAP168. ATC is not a pre-requisite. FISO and, under some circumstances, AGCS is adequate. For minimum facilities see
CAP393 Section 3 Page 8.
it looks like Lasham ...has some sort of radar
Decca (latterly Plessey) 424 Approach Surveillance Primary Radar. It is a private facility operated by an aircraft maintenance and repair organisation for its own purposes (non-public transport) and is licensed by the CAA. Service provision includes Traffic Service and Surveillance Radar Approach provided by CAA-licensed ATCOs. The radar has a narrow pencil beam. Traffic detection is dependent on the manual positioning of the beam therefore it is not suitable for Deconfliction Service. (The radar aerial Polar Diagram would have to be cosecant-squared or similar to ensure 'solid cover' with the additional disadvantage of detection of high-level overflights.)
to provide a radar service you had to provide an ATC service and to provide ATC you needed to be licenced
Provision of a radar service outside CAS is part of what is known as ATSOCA (See
CAP774). Where provided by civilian licensed ATCOs it is provided in accordance with
CAP493 and is subject to CAA audit.