It would be worth exploring how you intend to establish the "backhaul" link between the "extender" and the rest of your network.
"Proper" cabled ethernet would be best, in which case you need something called a Wireless Access Point (AKA "WAP" or "AP.") Or you can "cripple" and old SOHO router and use it as such (see "Using Two Routers Together" FAQ pinning in this forum.)
If domestic harmony precludes installig ethernet cables, then a backhaul tunneled over the mains electricity supply using HomePlug/Powerline technology is (probably) next best. In which case, have read of the "HomePlugs" FAQ pinned in this forums. Though it's doubtful you'd do it for GBP 30 unless you buy really old & slow variants.
If you are intending to use Wi-Fi for the backhaul then you need something called a Wi-Fi "repeater." These work by listening to the airwaves, copying each Wi-Fi transmission, waiting for the airwaves to go quiet, then broadcasting an almost verbatim copy of the original transmissions. Trouble is, Wi-Fi is an "only one thing at a time can transmit" technology and as such the "original" and "repeats" cannot occur at the same time, so repeaters can half, or worse, the throughput ("speed.") Thusly, repeaters have their use case, but we generally regard them as "least good" and to be avoided unless there is no alternative. Therefore, unless you have a "problem" with coverage, you wouldn't want to deploy a repeater "for the hell of it" as it would (probably) make your speeds worse, not better.