The answer is it depends. The list of shops allowed to remain open includes DIY stores and shops selling agricultural feed, supplies and equipment.
You can buy whatever you like in shops that remain open (ie you can legally buy nail varnish in supermarkets) so in theory there is no reason why you cannot go and buy a lawnmower in any shop that is legally open.
Remember however that the government calls on everyone to use their common sense, decide what is reasonable, and stay at home as much as possible.
Also, many DIY shops have limited the number of products they are selling, or are only selling by click and collect so you may have to choose online and then collect. You could also consider buying online and having a lawnmower delivered.
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