As you may or may not be aware, most internet connections in the UK use a system called Fibre To The Cabinet (FTTC) at the moment. In an increasing number of areas, a faster and more reliable option is now available - fibre to the premises (FTTP). However, finding out if this is available where you are can be quite confusing. There's a number of different FTTP providers, some who share lines with others, and some that don't. Just to take one example, in Horsham, some properties are already served by BoxBroadband and HeyBroadband. CityFibre have been laying cables in the town, and Openreach / BT is beginning their own rollout. Where can you go to check what's available to you?
UPDATE Feb 2022: Since writing this article, Thinkbroadband (mentioned below) have added an extra layer to their fantastic broadband map of the UK indicating if there's any FTTP provision for a particular area. This is now probably the best place to start before digging deeper into exactly which provider that is with the suggestions below:
https://labs.thinkbroadband.com/local/broadband-map#6/53.788/0.527/allfttp/altfttp/
Try Openreach's checker
The first place you might want to look is Openreach's FTTP checker here: https://www.openreach.com/fibre-broadband. Hit the "Check my availability" button and enter your postcode to find out if FTTP is available in your area now. If it is, BT and a number of other mainstream companies will be able to provide you an ultrafast connection right now (as Openreach resell their lines to many other organisations). However, the checker suggests you're not covered yet, that doesn't mean you can't get FTTP right now.
Check for local providers
This is where things start getting a little trickier. There are many other providers that have set up their own FTTP service - some of them hyper-local. Therefore, we can't list them all here. However, you may have some luck searching for your area and "ultrafast FTTP" for some hints on providers that have set up in your location. Once you know this, you can go to their respective websites and enter your postcode to see if you're covered.
Use ThinkBroadband's UK map
This is one will probably give you the most definitive answer and is an excellent resource, although is slightly arduous, so we've listed it last! First, go to Thinkbroadband's UK Broadband map here: https://labs.thinkbroadband.com/local/index.php?tab=2&election=1. Zoom in on your local area, then start ticking boxes on the right. Each of these selections relate to a specific broadband provider. In this case, you're looking for any with "FTTP" or "FTTH" in the name (in the case of Openreach, it's the "Openreach native FTTP" you'll want). If a selection overlays a series of circles in your area, that provider has set up shop in your location. This may apply to one or more providers in the list. Armed with that knowledge, you can then visit that provider's website to find out more.