Question about the British cabinet

I’ve heard it said many times that few members of the House of Lords will sit in the cabinet, and only in minor roles. However, I was reading something about the Falklands War and it noted the Foreign Secretary at the time of attack was Lord Carrington. So I’ve got some questions:
–Any other major posts been held by a member of the Lords in the past fifty years?
–Why did Thatcher pick a Lord for Foreign Secretary, and what was the reaction?
–How much of a problem is having a Lord as a minister on stuff like question time or dealing with the Commons?
–Are there any cabinet posts only a member of the Commons can hold?

According to Hugo Young’s biography of Thatcher, p 171-172:

It’s a bit more than 50 years ago, but before he became Prime Minister the Earl of Home served as Foreign Secretary in 1960-1963. (He famously renounced his peerage to become PM in 1963, and later served again as Foreign Secretary, but as a member of the Commons.)

To be very precise, Douglas-Home was appointed Prime Minister and then renounced his earldom. So, he did serve as PM (for a few days) while a member of the House of Lords, followed by a period during which he was PM without being a member of either House of Parliament.

There’s nothing to stop the Prime Minister leading the government from the Lords, but in practice it has not happened since Lord Salisbury’s administration more than a century ago.
As a peer, Carrington was not going to be a serious rival for her job.

From Tudor times until 2005, every Lord Chancellor (i.e. Justice Secretary), was a Member of the House of Lords. Now MPs can get back in on the act.

Personally, I wish they’d give it back to a peer…

Basically it is not problematic from a constitutional point of view to have a member of the House of Lords take a senior, more executive role in the Cabinet, but it is problematic from other angles though as there is an expectation inside and outside of Parliament that certain roles will be performed by elected members of the House of Commons and not unelected members of the House of Lords.

One of the most prominent recent examples is Lord Mandelson who was Secretary of State for Business, Innovation and Skills in 2008-2010 and First Secretary of State 2009-2010 (and hence the most senior Secretary of State). Though constitutionally there’s no reason that a cabinet member has to be a Member of Parliament, “Mandy” was only made a Life Peer just after being appointed to the Cabinet (technically for the third time, but the previous two times he was a Member of the House of Commons).

By strong convention, the Chancellor of the Exchequer must sit in the Commons. The last Chancellor to sit in the Lords was the 2nd Earl Spencer, who inherited his earldom in 1834 when already serving as Chancellor. He didn’t resign the office of Chancellor until four days later. The last Chancellor to serve any substantive period while sitting the Lords was 1st Viscount Stanhope, who sat in the Lords for about a year before he resigned the office of Chancellor.