Boring, out of context comment coming up - please prepare yourselves.
Lamb's Conduit Street was named after philanthropist William Lamb.
In 1577, he improved the conduit that brought fresh water to the people of area.
Interesting, also off-topic, information coming up.
I searched for the information moodywop asked for and at first found:
Вестимо где... Вот здесь: Alien's Registration Office, 10 Lamb's Conduit Street, London WC1N 3NX (Tel 0207 230 1208). The office is open Monday-Friday 9am-4.45. (Nearest underground station Holborn).
On further investigation, looking for an official site confirming its continued existence, I was very disappointed to learn that this office is now reserved for use only by extra-terrestrials and has been relocated to the dark side of the moon.
People-formerly-known-as-aliens are now advised:
Если ты находишься в Лондоне, то регистрироваться надо в Metropolitan Police Overseas Visitors Records Office или по старому Alien Registration Office по адресу Brandon House, 180 Borough High St., London SE1 1LH. Если не в Лондоне - то в местном Police Office.
What a come down - and it's not even in Sausage-skin Street.
It must have been such fun to tell your friends that you worked in the Aliens Registration Office!!
Busy day at the office?
Not really - couple of Venusians and a hitch-hiker from Pluto.
We're expecting a huge rush from that new planet they discovered the other day, though.
Final bit of off-topic information:
Alien Registration Office is also the title of a CD released in 2000 by AMP Studio. Not a lot of people know that.
I was going to list the tracks as well but perhaps not....
Meandering gently back towards the general area of the topic in the vain hope that this will save the post from the purge:
"...cut of his jib.." does, genuinely, appear in conversation from time to time. Now OK, some of the people I would have conversations with share some of my own eccentricities; but in the right context this would pass entirely without comment and would have expressed and conveyed meaning perfectly.
It's useful in reference to prospective job candidates or customer account representatives (salesmen

).
Thanks, Cuchu, for the explanation behind the meaning.

It is such a natural saying to me that I had never thought to wonder about its origins.