Another shout for Mantel here. Last few orders have taken two days, which is much better than I’m seeing from some UK shops at the moment, especially if they are using Royal Mail.
Wiggle Plus is very useful. For £10/yr, free unlimited next day deliveries. Annoyingly, they’ve brought the next day cut-off forward from 10pm to 4pm (2pm at weekends) and I’m not sure if this is a permanent change, or just a Covid-19 thing. That said, I don’t use Wiggle as much as I used to as I’m finding that they just aren’t as competitive as the European sites now. The switch to Hermes was worrying, but my local Hermes chap is pretty reliable so it’s not been an issue, but your mileage will definitely vary here!
Otherwise, will echo what others have said. Bike Discount, Rose, BikeInn, Mantel are all excellent and I’ve had no problems with any of them. Most now offer flat-rate returns, so if you do need to send stuff back, you’re not going to get stuffed for an expensive European courier.
In the UK, Merlin are generally quick to ship, but I am more wary of the likes of Winstanley, Tredz, Tweaks etc – sometimes their prices are very good and it’s worth the wait, but I’d never use them if I need something quickly as they invariably take days or even weeks to turn up!
And of course there’s St John Street Cycles – SJS – who stock the weirdest selection of spare parts, especially for Shimano kit. You want that obscure part for an old rear mech? SJS will be the place to go!
For me, the most useful tool is still Google Shopping for instant price comparison. Just be aware that it doesn’t have everything, nor does it always get things right, so sometimes you need to go fishing by yourself. eBay and Amazon can also be useful sources for parts, but (especially with eBay) watch out for very cheap parts that ship direct from the far-east. They may be absolutely fine, but will certainly take a lot longer to turn up – possibly many weeks – and returns will definitely not be an option here!
As you’ve noticed already, stocks are low, prices are high at the moment so be prepared to broaden your outlook and shop from further away!