If you intend to rent long term your best option is to raise the worktop subject to cost and getting permission,it looks like you would only need to raise it about an inch,it then gives you plenty of choices when looking at washing machines just give BEKO a wide berth.
the one you looked at can be seen on this website £372 inc vat
Your problem is likely to be depth. If you could get the fittings for an integrated on you would find that you wouldn't have enough depth. This freestanding one should be ok for height click here but I've no idea how good it is.