A "K" is a Knighthood.
There are different orders of kighthood e.g. the Order of the Garter (the top, they meet in Windsor Chapel) or a number of lesser types such as KCMG or Knight Commander of St Michael and St George.
Some where near the bottom of the Ks is he Order of the Thistle which is what Tony was rumoured to have been considered for (and despite being Scottish, was not at all happy about, especially as Margaret Thatcher became a Baroness.)
Below that are the "Gongs" like OBE (order of the British Empire otherwise known as "Other Bugger's Efforts) or MBE (Member of the British Empire; My own Bloody Efforts) and so on.
However, above knighthoods are Peerages awarded by the Queen which used to be hereditary and most/all of which are now life Peerages. (technically awarded by the Queen, but actually mostly by the Prime Minister in his New Years Honours).
This peerage used to entitle the Lord to sit in the House of Lords (till Tony Blair decided to change the system).
Actually, Tony is alleged to have discovered Life Peerages to be what is called " a nice little earner".
He, or his party, are alleged to have been receiving "Cash for Honours".
A number of his cronies and other rich folk donated huge sums to the Labour Party funds and would get Peerages, some also got posts in Government and some others got some other kind of benefit such as a lucrative contract to produce flu vacines or similar.
The only notional drawback is that this is illegal.
This isn't simply "not inhaling" but somewhat more serious.
A google for Cash for honours" should produce some background to this.
e.g.
Hence, while an honest Knighthood is pretty nice to get, an Honest peerage is even better.
The point being that Sir Frank had to wait for ever to get his honest knighthood but got next to nothing financially. If he had been properly recompensed for his invention i.e. what he could have expected if he had been allowed to profit from it himself, then he could have bought himself a peerage. Except, as a man of integrity he wouldn't have even considered it.
JMW