What is often totally misunderstood is what/who affects your internet speed. These are in order of importance and ease of fixing (hardest first):
a) The actual 'line speed'. In most cases, the last section of a line is provided by Openreach for non-cable connections. If you get 20Mb from one provider, changing provider will do nothing to change the line speed because that is unchanged - the copper between your house and the cabinet/exchange is the same. So BT FTTC and other provider FTTC will be pretty much the same speed.
If you can't get FTTC and are on an older ADSL2, then your speeds will be lower.
Each provider can do some minor things to tweak line speeds and some provider routers are better than others but if the link is slower than it should be for the length of copper between your house and the far-end you are not going to get major gains by switching provider, unless you can get someone to fix the line issues, which will have to be done via Openreach.
The line speed is the maximum you'll ever get and is constant from you to the cabinet (or exchange) at any given time. It may fluctuate as your router and the provider kit try to get stable link. Be aware that at this time of year, your line speeds are likely to take a hit from all the RF interference that comes from Christmas lights and water/cold weather affecting the physical cabling. Oh, and streetlights in some places. We can tell the time of year from line noise/attenuation graphs.
If you have cable, then its a whole different set of issues due to the way it is delivered and your line speed may actually vary, so you have to pick cable or copper. If you have FTTP then it should be better and as you have a full fibre connection, it should be clear of the interference issues and be a pretty much constant speed (assuming you've recovered from the install fees if you aren't in the middle of a major city)
b) Provider connection, congestion or poor backhaul. Changing provider can affect this, if you are getting major packet loss or issues with data transfer at speeds below the line speed. Some are better than others, provide better router etc. Mostly changing provider will help if you get peak-time issues (congestion) or the router is rubbish, though buying your own router is also an option if that's the issue.
You're probably also using your provider's DNS servers, which may be overloaded at times, so you can try using Google or Cloudflare DNS servers as that might speed things up.
Provider filtering/bandwidth limiting is less common now, but does happen for 'network protection' and avoiding excessive use, so worth asking if this happens.
A very common issue during school holidays is that your kids that constantly stream stuff and torrent things which then affects your connection, as they're using all the bandwidth! If everything gets better late evening (if you have young kids, after they're in bed) or morning through to lunchtime-ish (if you have teenagers when they're still in bed!) then parental controls may be needed.
c) Wifi connection speed. Routers/access points vary in effecitveness and how they cope with multiple connections and local interference. This can be far worse in housing estates and blocks of flats. Test anything on a fixed ethernet connection and if it is better then you have a Wifi issue. Changing provider in itself won't help, unless is is a router issue. Often moving the router can help more than changing provider. If you live in an old stone cottage with thick walls or a steel built structure or have a really large house then you may need to look at a mesh wifi solution to increase coverage. The further you are from the router, the slower your connection will get as the signal gets weaker.
As a final comment, the fancy gaming routers don't do a lot more than normal ones and the idea that a mega router can make a huge difference to gaming performance just isn't true. Router packet switching delay is so low it is undetectable in any decent router. NAT processing and firewall is so quick these days it just isn't an issue. At most you may save a few microseconds, which makes no real difference given the time taken to get packets across the internet to the gaming servers and it wasn't the reason that 8 year old killed you in Fortnite