Microwave ovens aren't on the list of prohibited waste on the website of a local skip hire firm in this area:
https://www.collins-skiphire.co.uk/domestic-skips
As that firm is simply complying with national legislation, it's likely that other skip hire companies will have similar rules.
However all retailers of electrical and electronic goods are obliged to accept similar goods for recycling, even if the goods haven't been sold by them. (The only exception is where the retailer has paid a fee to be exempted from the scheme). So, for example, you can take your old microwave oven to any branch of Currys/PC World; they can't refuse to accept it.
Further, most household waste recycling centres (a.k.a. 'tips') have an area reserved for 'small electricals', such as TV sets, PCs, monitors and microwave ovens.
https://www.recycleyourelectricals.org.uk/electrical-recycling-near-me/