You're right, this isn't a feature that you'll find on many cars this size, but it's possible.

You can fit the BMW 1 Series with electric memory seats for £750 – with electrical adjustment for height, backrest tilt, seat position and seat base tilt. The memory function means by pressing a button your seat and exterior mirror settings can be returned after someone else drove the car.

For £1500, BMW's Comfort Pack 2 bundles the electric seats together with an electric opening and closing boot that you may find handy. The pack also adds keyless entry and a heated steering wheel as part of the deal. Finding a second-hand car fitted with this pack will likely be easier than finding a car with just the electric seats fitted.

The Volkswagen Golf can also be had with electric seats. They're an option that's only available on higher-end models – starting with the GTI – in combination with leather upholstery. The option costs £2130 in the GTI and gives you electric adjustment for the driver’s seat height, seat length, seat cushion angle, backrest angle and lumbar support. The VW's seats also have a memory function that returns your seat and mirrors to their original position.

Finding these packs on either car will be easier to do at a franchised dealer which will have a comprehensive database of the options fitted to the cars it has in stock – some non franchised dealers do also offer this.

Both the BMW 1 Series and Volkswagen Golf have recently been updated and the current new car shortage means both command strong residuals, you may struggle to find a car for £20,000. The good news is that electric seats were also offered on the older models that are in your budget.

If you want as new a car as possible, I'd recommend the new Peugeot 208 – it's a small car that's pretty big by the standards of a few years ago.

GT and GT Premiums models are available with optional Nappa leather seats that have driver seat multi-way electric
adjustment (including electric lumbar adjustment) and a massage function. They're also heated. GT models built in 2021 with around 10,000 miles on the clock are currently on sale for just under £20,000.