Great question.
To begin, the following passage from Britain, the common wealth and the End of Empire by Dr John Darwin discusses the "staggering blow" Great Britain felt after granting independence to India.
…
The huge sense of relief at a more or less dignified exit, and much platitudinous rhetoric, disguised the fact that the end of the Raj was a staggering blow for British world power. Britain had lost the colony that had provided much of its military muscle east of Suez, as well as paying 'rent' for the 'hire' of much of Britain's own army. The burden of the empire defence shifted back to a Britain that was both weaker and poorer than it had been before 1939.
Britain was overshadowed by two new superpowers, the United States and Soviet Union.
...
Source:
Britain, the Commonwealth and the End of Empire By Dr John Darwin (Last updated 2011-03-03)
That being said, after reviewing the unemployment rates for Great Britain (The United Kingdom) in the years following the independence of India (beginning in 1947), it does not appear that the rates changed as compared to the early 1940's.
Average Unemployment Rates, Nine Countries, Six Major Periods, 1904-1950 CHART2 pg 458.
In fact the unemployment rate dropped from 2.5 (1946) to 2.0 in 1947.
INTERNATIONAL COMPARISON OF RATES TABLE 1 pg 456
As noted on page 462 the wartime employment rates neared 100%. Not noted but possibly assumed, post wartime employment rates remain high due to loss of life during wartime as well as job availability in disaster recovery (which certainly was evident in post war Britain after WWII.)
It seems that the public reaction to the labour party's direction to providing a welfare state was not met with huge opposition. In fact the voters wanted an end to wartime austerity
The Labour party, after winning the 1945 elections began the process of dismantling the British Empire when it granted independence to India and Pakistan in 1947, followed by Burma (Myanmar) and Ceylon (Sri Lanka) the following year. These movements along with others parallel the Fabian Movement. The Fabian Society laid many of the foundations of the Labour Party and subsequently affected the policies of states emerging from the decolonisation of the British Empire, especially India.
In conclusion, I would say that as a whole Great Britain did partially suffer in terms of world power, by granting independence to India . However, without the internal stability needed to enforce colonial or Imperial rule over India, (as well as other countries/states) India would not have provided the benefits Great Britain had once received. In regards to the return of British natives from India, I see no evidence to suggest that unemployment rates during this timespan rose. Also, as previously noted the ideas of the Fabian movement, which were pursued by the newly elected Labour party, do not seem to have been met with enough opposition to suggest there was a negative public reaction to the dismantling of the British Empire or those returning from said Empire.