It's a no brainer. Spend some cash to give every MP something like Sametime Connect (like Skype but industry strength and encrypted). While Palace of Westminster is made safe, have every MP dial in to The Commons every day, and broadcast, so he/she can be seen at his "desk" "working". Any MP not broadcasting, display as "Member for eg Chiltern Hundreds Absent" so that constituents know it.
No rail fares or second residences in London, available for constituency surgery five minutes after broadcast.
Palace of Westminster becomes redundant, use it as a tourist attraction to put money into the Exchequer. Save an arm and a leg.
Committees etc? Dial in to the appropriate meeting. Jobs a good 'un.
Edit. House of Commons, welcome to the 21st Century.