I don't think anything like this is still made. An old Sony ICF-5900W would fit the bill, with a decent dual conversion tuner and built in BFO (though it has no LW). These are still quite common secondhand, and while they're not cheap you should be able to find one for less than £100. They don't share the reliability problems of the later (smaller) Sony SW sets which use surface mount components.
https://www.radiomuseum.org/r/sony_icf_5900w.html
The cheapest solution is to build a simple external BFO (one transistor and an IFT) and use it with any domestic radio with SW coverage, but it can be tricky to stop the BFO signal swamping reception.