I think this is now a more or less comprehensive list of the 35C+ stations (Met stations plus airports), minus any manual additions later.
Cambridge 38.1C (via Met Office - no synop)
Cambridge Airport 38C^*
Kew Gardens 37.9C (via Met Office - no synop)
London Heathrow 37.9C
Writtle 37.7C (via Met Office - no synop)
Northolt 37.6C
Lakenheath 37.1C*
Benson 37.0C
London City Airport 37C^*
Luton Airport 37C^*
St James's Park 37.0C
Stansted Airport 37C^*
Mildenhall 36.9C*
Wittering 36.7C
Rothamsted 36.6C
Marham 36.5C
Cranwell 36.3C
Reading University Whiteknights 36.3C
Santon Downham 36.3C*
Woburn 36.3C*
Holbeach 36.1C
Nottingham 36.1C
Teddington 36.0C*
Brooms Barn (Bury St Edmunds) 35.9C*
Langdon Bay 35.9C
Andrewsfield 35.7C
East Malling 35.7C*
Farnborough 35.7C
Cavendish 35.6C*
High Beech 35.6C*
Stowe 35.6C*
Sutton Bonington 35.6C*
Bedford 35.5C*#
Frittenden 35.5C*
Manston 35.5C
High Wycombe 35.2C
Odiham 35.1C
Scampton 35.1C
Waddington 35.1C
East Midlands Airport 35C^*
Finningley 35C^*
Herstmonceux 35.0C
Lydd Airport 35C^*
Oxford Airport 35C^*
Southend Airport 35C^*
* Highest hourly reading
^ Value to nearest whole degree only
# Bedford weather station stopped reporting after 1pm reading, this is the highest value up to that point.
Originally Posted by: Rob K