I agree that there should be a completely new Parliament Building but think it should be built in the Centre of the UK. By my calculation that would be slightly North West of the Scottish Border in Dumfries and Galloway, though I understand that the recognised place is Haltwhistle in Northumberland, just south of the border.
So at a location near the West end of the border with good road, rail and air links, a purpose built or commandeered set of buildings to consist of two debating chambers, one of which should be big enough to accommodate all MPs at once and wired up such that MPs can vote from their seats. This is the case in the Scottish Parliament, where MSPs can only vote if they have been present in the chamber during the debate.
There should also be provision of a bedsit/office for each MP on site so that there would be no need for second homes. Also a media centre, some reception rooms, a cabinet room and committee rooms, a nice garden or park, perhaps a fitness centre, foodcourt and supermarket and temperance restaurants. I suppose the PM could have a separate, larger residence cum office, where visiting dignitaries could be entertained. If there was pleasant countryside around then the accommodation could be let out to tourists during the long Summer recess.
Hand over the Palace of Westminster to the National Trust and they could fund-raise to pay for renovations. Job Done.