Well I'm back from our 11 days - it was perfect, as always!
On the practical COVID stuff
Before leaving home - filled in Iceland pre-registration form (links to your mobile number/email address), received bar code and downloaded the Rakning tracking app. Also ordered day 2 test for when we were back as you need the booking ref to add to your UK passenger locator form.
At Heathrow - showed NHS App to prove vaccination status and barcode for pre registration
At Keflavik - went through usual passport checks then there were additional desks in Arrivals. Showed NHS App and barcode again. As this was June, barcode was linked to a test tube I was given for PCR test. Then went to portacabin in the car park and nurse did throat and nasal swab.
Picked up rental car and drove to first accommodation. Got a text message with negative result for test (4 hours and 22 minutes from test to results)
For return test to UK we registered and paid for the rapid antigen test on www.COVID.is and booked a test for the day before our flight at 8.30 in Reykjavik. This was 4000isk/£23 each.
We were staying near Hlemmur bus station and test centre was at least 30 minutes walk from there away from city centre so we drove round. Joined the queue (need to wear masks until the test) at about 8.15 and we're in and out quickly (similar process to at the airport with barcodes and test tubes but just a nasal swab done by a nurse). By the time we'd driven back to the apartment we both had emails with the negative certificate.
Return flights were similar - showed UK passenger locator and antigen cert at Keflavik (need to wear masks in the airport still) then same at Heathrow before going through passport e-gates. 10 minute queues at both.