The biggest impediment to improving the roll out of Fast Broadband is that each of the two players guard their local loop like the crown jewels and do their best to keep the competition out.
" being the key word here.
Its Virgin and BT's property, no-one else's.
There's a multitude of issues with your proposal.
1) How can you force any private company to sell what they own?
2) Who would buy the combined BT and Virgin infrastructure, the government?
3) Who could afford to buy the combined BT and Virgin infrastructure?
4) Should this even be possible, who would still be the biggest customers of this company. BT and Virgin..... (re your influence issue)
Its like saying... the biggest impediment to improving the mail and parcel distribution service in the UK is to make the Royal Mail sell all of their post boxes and distribution depots to another company and let UPS/TNT/<insert courier here> all use them
Why? Its Royal Mail property, who has any right to make them sell it? Same with Virgin & BT