Can you work in one country and live in another?

[Camomila]

Just idly wandering (mainly based on the threat of no deal + how cheap nice flats are in my nearest 'naice' town in Italy)

Can/do people work from home for a British company while living in the EU?

I imagine if anyone would know it'd be the Brexit board. Although, I imagine everything will change post Brexit.

Awaits being told it's a legal/tax nightmare!

[VenusOfWillendorf]

This varies from country to country but is certainly possible. The easiest is NI/ROI as there's an agreement in place to treat the citizens of each the same as home citizens. That will stay even if there's a no-deal brexit.

The rest have different regulations. But whether you pay tax in a country depends on how many days you spend/work there. Currently, you only pay tax once, but who you owe it to can be split between two counties if you are moving between two.
I live in Switzerland, near the border. Many people commute daily from France and Germany. We can work from home, but theres a rule that people living in F/G can only work a max of 24.9% from home, as any more makes social insurance deductions too complex as split between the countries. For income tax, people are taxed on where they live, not work. I also have a friend who lives in Switzerland but works in the UK quite a lot as her company have an office there. If she spends over a certain number of nights in the UK, she gets a tax bill from the UK.
Neither example is useful to you, but just to show what's possible.

[spinn]

The uk currently has agreements with many countries regarding tax to avoid double taxation. You need to do some googling around that to see if it works in your scenario....whether it will work after Brexit is a whole other scenario.

[Ofitck]

I know quite a few people who live in France but work in Spain. And also some people who live in spain but work for British companies.

[mackerella]

My brother does this - he works for a UK company (he's British) but is resident in a different EU27 country (where his wife is from, and where his kids have citizenship). BUT... he has to work in the UK for 2 weeks of every month, in order to satisfy some employment or tax requirement. As his company is near to where my parents live, he stays with them while he's in the UK and commutes to the office from there. He works from home in the other country the rest of the time.

The advantage is that he can earn a much higher wage than he would in the other country (which is one of the newer EU states) - although this is being severely eroded by being paid in GBP while living in the Eurozone! But he's away from his family for 2 weeks every month (more like 12 days if you can get good flights), and the travel is both tiring and expensive. He's also jeopardising his right to stay in his resident country as he's now no longer working there and, post Brexit, won't automatically be able to live there!

Some of this won't apply to you if you have an Italian passport, but I'd look into whether you'd be required to work in the UK part-time if you're an employee of a UK company. I guess you could get round that by being a freelancer, but then there would be tax issues to sort out in Italy.