I have a cheapy TP-LINK from Amazon.
Works brilliantly all over the house.

This is the one i use..

That's not a router, it's just a WiFi adaptor.

It just enables your PC to access a WiFi router

Mine is just the bog standard Movistar router....it works just fine!
I can even use my laptop out on the terrace, which is just about as far away from the router as it's possible to get, and I don't have any problems even there.

We also only have a bog standard Iberbanda router and no problems anywhere.

I've had several wireless routers over the past few years and to my shame, it's only in the past few months that I've come to realise that the wireless output of routers can differ quite significantly between models. I thought they were all just "wireless" and pretty much the same.
Reading online reviews I was surprised to find that wireless performance could vary so widely between models and that on some, it is possible to adjust the wireless output as well as other settings routers towards the lower end of the market don't permit.
I'm not thinking of changing mine just at the moment but when I do, I'll certainly do a lot more research than I have done before as I do when choosing other products.
If therefore, wireless range is an important factor in a router I would advise researching the ones which provide higher performance in this area.
Apologies if I'm just stating the obvious!

Yes they can vary and the latest n spec ones are supposed to give better range but I can't say I noticed much difference when I upgraded.

The simplest option is to spend €25 on a range extender combined with a cheap router.

Those sort of ads and claims make me laugh.

One of the underlying rules of thumb for antennas is that the more you have the more you get - bigger dish gives you a stronger satellite signal for instance - and most of the products which claim x dB gain are simply not physically big enough to produce that.

Worse, at the sort of frequencies WiFi works at the choice of coaxial cable is crucial and generally the type commonly used by these antennas is rubbish and will probably be introducing losses in excess of the gain claimed for the antenna proper leaving you with a net overall loss !

Some user will claim near miraculous results from these devices but I would be willing to bet that in the majority of case any improvement have been as a result of the external antenna being in a different place and if the actual router itself had been located there similar improvements would have ensued.

FWIW, and to illustrate the gross inefficiency of consumer WiFi products, given the correct antennas and cable it's entirely feasible to establish a 100% reliable high speed WiFi link over several kM, and that with as little as 50mW of transmit power, half that of the typical consumer WiFi router.

Over a sea path you could work to the horizon which, given an antenna height of 5m at each end, equates to a shade over 11kM.