I would say if you’ve got £80 to spend I wouldn’t do espresso. My recommendation for an entry level machine would be something like the Rancillio Silvia. It’s still only a single boiler machine, so you won’t be able to steam milk and pull a shot at the same time, but it’s built like a tank and makes decent espresso. They come up on eBay occasionally for around £250.
The machines you can buy for £80 are unlikely to make great coffee. I’m sure it’s possible, but it is likely to be frustrating and will need a lot of skill to do. It’s like buying a cheap single-vessel system. They exist but are usually poorly made, inaccurate at holding temperatures and prone to breaking. The more you spend (up to a point) the more consistency you are buying with your money.
You can make great coffee with a stove top, or a French press or Aeropress for that matter. The most important thing I would do if I wanted to improve my coffee for £80 is to buy a decent grinder and grind your own beans. I think you’ll find this will do far more to improve your cup quality than buying a cheap espresso machine.
For £80 I would get something like this:
http://www.madebyknock.com/store/p50/Aerspeed.html
I would strongly advise you to avoid electric grinders at this price point.
Without grinding your beans yourself you won’t be able to make good espress for two main reasons, freshness and control of extraction.
1. One ground, the aromatic compounds in roast coffee oxidise within a few minutes. To test this yourself, compare the smell of a freshly-opened bag of ground coffee from the supermarket to one that’s been sitting open for an hour or two. Similar to hops, coffee needs to be fresh.
2. In order to make good espresso you need to dial in the grind to your machine to ensure the coffee is being extracted from the grounds at the correct rate. If the grounds are too fine, you’ll have an over extracted, ashy cup of coffee. If the grounds are too coarse, you’ll have an under-extracted, sour/salty taste, with little crema. If the whole bag of beans are already ground to a certain size you won’t be able to adjust this and will instead have to manipulate the dose of coffee instead in order to regulate the flow of water through the puck, which is like trying to adjust IBUs by adding water to a pint of beer. You can do it, but it’s not the best way to solve the problem.
If you have any coffee questions I’d love to help! Like beer, it’s something I really enjoy
I also appreciate you have asked for advice about an espresso machine and I have instead told you about a grinder... so feel free to ignore everything I’ve said.
Lastly I’m sure you’ve seen this video from James Hoffman, it really changed how I approached stovetop coffee: