Thanks for all your input. In case anyone is reading this in the futre and has the same problem, someone from a techie forum suggested a workaround that uses the laptop's spare USB3 output to act as a second HDMI display port:
https://www.amazon.co.uk/dp/B00H91B...LYLB2HP7&psc=1&ref_=list_c_wl_lv_ov_lig_dp_it
So with that adapter, both screens could plug into the laptop without using a dock. But as it's around £40 and we already have a wall mounted dual arm laptop/monitor stand, we are going to stick with that. I'm not even 100% sure the above will work, as apparently our Lenovo laptop is the most entry of entry level machines