Rhodesia
"Illegal stamps"

As a reaction to the unilateral declaration of independence of Rhodesia on November 11, 1965 British postal authorities regarded Rhodesian stamps issued later as "invalid" although this was not justified by UPU rules.

Formular aerogramme sent from SALISBURY (24 JAN 1966) to London, UK for philatelic purposes. The postage paid was 
6 d.
 
The calculation of postage due in the “Rhodesia case” did not follow uniform rules. According to information compiled on stampboards.com the rules were:

• 8 Dec 1965 - Apr 1966 : Double deficiency surcharges based on correct postage required less the value of any legal stamps present
•  
• 17 Feb - 8 Oct 1970 : Calculate the correct postage less the value of any legal stamps used; double this value; convert the result to sterling at 1c = 1.4 d

The stamp on this airletter was regarded invalid and the aerogramme was taxed with double the deficiency (12 d = 1 s). A boxed green handstamp was applied: “INVALID STAMPS / USED / POSTAGE DUE ...”, “1 s” endorsed and a 1 s UK postage due stamp affixed.

Another aerogramme from Rhodesia from a later period and some background of the "illegal" stamps can be found here.

Rhodesia
"Illegal Stamps"

This aerogramme form was sent from BULAWAYO (10 APR 1970) to Brighton, UK. The postage paid was 7.5 c.

“Although prepared to grant formal independence to Southern Rhodesia (now simply Rhodesia), the British government had adopted a policy of no independence before majority rule, dictating that colonies with a substantial population of European settlers would not receive independence except under conditions of majority rule […] On November 11, 1965, following a brief but solemn consensus, Rhodesia's leading statesmen issued their country's unilateral declaration of independence (UDI).This was immediately denounced as an "act of rebellion against the Crown" in the United Kingdom.” (Wikipedia).

As the UPU always regarded Rhodesian stamps as valid, this seems to be an isolated action of the UK government.

The calculation of postage due did not follow uniform rules. At the time the aerogramme was sent, the rule was: Calculate the correct postage less the value of any legal stamps used; double this value; convert the result to sterling at 1c = 1.4d

As all stamps used on the aerogramme form were regarded invalid, double the deficient postage was 15 c converted into 1s 9d at a rate of 1 c = 1.4 d. A boxed green handstamp was applied: “1’9 To PAY / POSTAGE UNDERPAID” and three UK postage due stamps (1s, 6 d and 3 d) were affixed.
 
Unfortunately, this is only the front panel of the aerogramme.