I was always taught a microlight is disallowed to enter any controlled airspace, whether radio or transponder or dishwasher or whatever installed and/or operative. Of course the UK will have its own rules.
In practice it appears one CAN request entering controlled airspace, and depending on equipment, controller's mood and probably other factors it MAY be granted. Radio and class C transponder seem the minimal requirement to entertain any hopes.
A curious exception is in the Belgian AIP for Ostend EBOS:
5.3 ULM FLIGHTS
ULM flights will only be accepted within Oostende CTR if the traffic situation permits.
Take-off and landing is only allowed for ULM aircraft complying with the following:
- three-axis ULM
- Equipped with transponder
- Equipped with radio able to communicate on VHF
- Able to maintain an airspeed of 80 KIAS MNM