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Might be a little over budget, but you could get this kettle if limescale is a massive issue
The kettle itself is £30 which is in your budget only just, but it has a Brita filter in it which needs to be replaced every month. You can get knock of brand filters from Tesco 3 for £5, or on Amazon 5 for £15. Brita brand ones might add up a bit.
Also the water you boil will now be soft water. Many people prefer this but your tea won't taste exactly the same if you're used to hard.
Not sure about this temperature control whatsits malarkey but get yourself a quick kettle. No one should be left waiting for their tea.
(The ones with the glass sides though, I think they look rather fancy on the kitchen worktop and you can more easily see how much water you have left).
(Behold!)[Russell Hobbs 22851 Brita Filter Purity Electric Kettle, Illuminating Filter Kettle with Brita Maxtra+ Cartridge Included, 3000 W, 1.5 Litre, Plastic https://www.amazon.co.uk/dp/B01GFPWHZ4/ref=cm_sw_r_cp_api_glt_i_CJK5V3PRDE9P9H0GTDB5]