All of KLM’s EHEH and EHRD flights are F50s, Luxair use 145, as do BMI. Lufthansa use both RJ85s and CRJs. LOT sometimes bring in an ERJ-170.

Regarding ‘bans’ on traffic…..from the EGLL UK AIP entry….

Operators of General and Business aviation aircraft may only operate in the peak during any operating season
if they obtain permission to do so from the airport operator as well as a slot in advance of each movement also from the airport operator.
In practice, permission to operate in the peak will be deemed to have been granted under the terms of the Traffic Distribution Rule
(copies available from Manager Heathrow Operations Centre, Heathrow Airport Limited), if a slot for each movement in the peak is
granted. Operators of General and Business Aviation aircraft, who arrive and depart at any time, may operate the movement provided
that the aircraft departs or arrives to the approved slot time. Those who fail to operate to the approved slot time or who operate in the
peak without first obtaining permission and a slot from the airport operator, are liable to be prohibited from operating in the peak
thereafter, unless the airport operator is satisfied that the movement amounted to an emergency or other circumstances beyond the
control of the operator or the commander of the aircraft. This permission will not be given for flights for recreational, charity and record
breaking purposes. Light single and twin engined private aircraft will not be permitted to use the airport. Applications for prior
permission must be made not more than 10 days and not less than 24 hours before the proposed flight and should be addressed to the
Manager, Airport Co-ordination Ltd,