VAT Refund at London Airport for EU Purchases?

No, you can't. You have to apply while in the EU. The UK is no longer in the EU.

VAT refunds

If you are resident outside the EU you are entitled to a VAT refund on goods you have bought during your stay in the EU if the goods are shown to customs on departure within 3 months of their purchase together with the VAT refund documents.

The process itself (i.e. the claim and refund) is not harmonised at EU level. This means EU countries may apply different procedures, depending on whether the seller of the product and/or a third party (‘VAT refund operator’) are involved (at the time of purchase or after).

All claims must be validated by the customs authority (either digitally or physically) before you leave the EU. Be aware that some countries set a minimum value of purchases or other criteria to qualify for a refund.
https://europa.eu/youreurope/citizens/consumers/shopping/vat/index_en.htm

I suspect not.

Before you leave France or Italy to come to the UK you will need to process the VAT. You should be able to do that depending on the airport/train station you use.

I have done it several times at Gare Nord when taking the Eurostar to London.

and you must have the form from each place - each store - you purchased at. Some stores do it and some don't.

You say you bought these few items in both Italy and France. Do you have the form for each?