I just got a new basic hardtail bike. I want to get better, and it’s not the best bike, so I want to upgrade it. I was thinking about changing the gear set up to 1 and 11 speed rather than 3 and 8 speed. I go out about mountain biking twice a week, and I really like it. My budget is £250. Any suggestions?
Switching from 3x8 to 1x11 would be an expensive upgrade, well beyond your budget unless you get lucky hunting for used equipment, and may require a cascade of upgrades you hadn't planned on, which increase the cost further.
You'd probably be better off saving up for a new bike--bike manufacturers are able to get parts at much lower cost, so when you buy a complete bike, you're getting the parts more cheaply than you could get them as an individual.
Disclaimer: I am not a fan of upgrading bike components. I believe for most people, it's a waste of money, usually trying to make a silk purse from a sows ear. Some succeed, but few do better than using the money to upgrade the entire bike. (Replacing worn out components with better ones can be worth while if done carefully.)
With just two years riding and £250 to burn, here are the options I would consider, in order of impact on enjoyment and speed when riding.
Yourself: spend the money on coaching and joining a club where you get to ride with better riders than yourself. Look into nutrition and decent cycling clothing if you have not already done so. Maybe join a gym if your fitness levels are lower than ideal (but to be honest, riding is a much better way to get fit for riding). A skilled rider on the crappiest bike will out perform an untrained rider on the best bike.
Dropper post: Unless you are riding mostly non-technical XC, a dropper post, especially for a relative novice, is a big advantage.
Brakes: For anything more technical than bike paths, decent brakes allow you to ride faster into corners with more confidence. The more confident you are you can scrub speed in a hurry, the faster you will hit the apex, the faster you come out. More fun and quicker times for less effort.
Stash the cash and start saving. Ride the bike you have until you can afford an upgrade of the entire bike. A 3x8 in decent quality dates back to mid 1990's. If newer than about 10 years, 3x8 is probably a cheap, low quality Mountain bike.
1x setups are a bit more than shiny bling, and here to stay, but they do not make a bike significantly faster or more fun to ride. The advantages are more from removing the mechanicals from the stressed and crowded BB area of modern squishies, allowing frame designers more options. If you must spend money on a 1x drive train upgrade, look at the Microshift Advent 9 speed.
Before spending money, watch a few of the "Cheap/Walmart MTB" videos on YouTube (e.g. the one below) and see what a cheap bike can do in the right hands.
I second (third?) the suggestion that you not spend the money putting a 1x11 on a cheap bike. I agree that it would be better to continue to ride the 3x8 drivetrain and wait for a new bike that is already 1x11 (or 1x12, or 1x15 or whatever the industry is into by then). Short of buying a new bike/frame, here are my suggestions for cheap-ish upgrades, making a couple of assumptions as to what you already have:
New pedals. Most lower-end bikes come with cheap plastic platform pedals. I would recommend you get a set of clipless pedals and spd-compatible shoes. You can find both fairly cheap these days, and they can be swapped over to a new bike whenever you finally upgrade. You can handle the bike a lot better and generate a lot more power with clipless pedals. If being attached to your pedals intimidates you (and it shouldn't), even an upgrade to a good quality flat pedal with metal pins will make a world of difference.
Tubeless tires - Fewer flats, lighter, ability to run lower tire pressures. There really is no downside to tubeless once you have them set up.
Brakes - hydraulic disc brakes will give you a lot more confidence on the trails. If that is not in the budget, I'd go for an Avid BB7 mechanical disk brake, which gets close to the same performance for half the price.
Dropper post, but only if trying to go very fast on the descents is a priority for you.
If you don't already have one, a good helmet jumps to the top of the list. All your new parts aren't worth anything if you're brain-dead.
The best upgrade you can do to a mountain bike is tubeless ready wheels and high quality tubeless ready tyres. It really can transform the way a bike performs.