You can file a claim in Small Claims Court in the UK. Delta are legally responsible for your loss and as your journey originated in the UK and your ticket was bought in the UK, there is no problem filing here. The costs are relatively small and you can do it all online. You can also complain to the Air Transport Users Council. You can claim for your losses.. hopefully you will have some receipts for the gifts. In addition, you can claim your additional costs of purchasing new items at your destination.
Here are the links:
For the online Small Claims court, you can file your claim here. You do not have to appear and it is likely neither will Delta. However, if they fail to respond you will have a default judgement against them. You can then do to Heathrow and impound their aircraft if you want to until the claim is settled!! That would be great TV!
https://www.moneyclaim.gov.uk/csmco2/index.jsp
The Air Transport Users Council is a quango I think but can also progress your claim on your behalf.
http://www.auc.org.uk/