It is not Peter's it's mine.

Actually, it seems to be NCP's it used to be Peter's Building, 11 Rumford Street or 1-3 Chapel Street, between Rumford St and Covent Garden, behind the Pig and Whistle.
I had always assumed it was a bomb site and with the proposed building of a multi-storey car park on top of the Victoria Street car park, which is the former site of the Government Office, which was destroyed during an air raid in WW2. I thought I had better find out something about Liverpool's last bomb site, turns out it isn't one. The OS Map for 1953 has it intact and gave me the name Peter's Building. A quick search of the planning system revealed an application "To use office room No 12 on ground floor as a stationery store room", approved on 11/11/1965
Which led me to some information that suggested it was still up and occupied in 1968.

A search revealed a THE LONDON GAZETTE, SEPTEMBER 1970 notice post by a Forwood Williams & Co of Peters Building

A little bit later and the same London Gazette takes it to 1973 here.

This from 1983 is interesting and might show ownership but no indication the building is still there. WINDSOR SECURITIES LIMITED

All that is left. ReptonX
You would think a building that existed in 1973 there would be some photo of it somewhere and someone would know what happened.

Sometime later

09-10-1974 Approved development of offices which is like why the building was demolished, no permission would have been needed for demolition.
To redevelop the site of Peters Buildings 1-3 Chapel Street/6-12 Convent Garden/9-13 Rumford Street by the erection of a building comprising six floors of offices with ancillary basement car park and including a (replacement) public house and two kiosks (total overall floorspace 9370 square metres total height above ground 30 metres) 

14-04-1976 A bit more searching of the planning site reveals an approved development plan in 1976
To redevelop site by the erection of a building comprising seven floors of offices with caretaker's flat above and basement car park and including a replacement public house and two kiosks for the purposes of retail sale with in Class I of the Town and Country Planning (Use Classes) Order 1972 (total overall floorspace 9796 square metres) 

Office development in 2 phases 

Since then nothing, there do not seem to be any underground works that would stop a big building being built.


Given it location it is surprising it has not been redeveloped perhaps it is too small for the office space some claim Liverpool requires. but it would make an ideal site for a multistory car park, which could combine the capacity of this space with that of Hackins Hey.