I find it was 40% of government expenditure, not of GDP. I find GDP in the mid-1830s was about Ł500 million, thus government expenditure was a tenth of GDP and the slavery emancipation compensation fund was about 4% of GDP (about half of what ATinNM estimated for the US). I suspect your figure of about $7bn for US GDP is government expenditure, too, given that ATinNM wrote above that 1860 US GDP was estimated at $88bn. At any rate, the war expenditure (here estimated at $6bn on the Union side and $2bn on the Confederate side, without veterans' benefits) was about the same as the value of the slaves as estimated by ATinNM. IIRC the Team of Rivals book had an estimate on the money actually intended for Lincoln's 1861 compensation scheme, I'll check it in the evening when I get home.

On the beneficiaries of the compensation in Britain, I found this:

Britain's colonial shame: Slave-owners given huge payouts after abolition - Home News - UK - The Independent

Academics from UCL, including Dr Draper, spent three years drawing together 46,000 records of compensation given to British slave-owners into an internet database to be launched for public use on Wednesday. But he emphasised that the claims set to be unveiled were not just from rich families but included many "very ordinary men and women" and covered the entire spectrum of society.

Dr Draper added that the database's findings may have implications for the "reparations debate". Barbados is currently leading the way in calling for reparations from former colonial powers for the injustices suffered by slaves and their families.

Among those revealed to have benefited from slavery are ancestors of the Prime Minister, David Cameron, former minister Douglas Hogg, authors Graham Greene and George Orwell, poet Elizabeth Barrett Browning, and the new chairman of the Arts Council, Peter Bazalgette. Other prominent names which feature in the records include scions of one of the nation's oldest banking families, the Barings, and the second Earl of Harewood, Henry Lascelles, an ancestor of the Queen's cousin. Some families used the money to invest in the railways and other aspects of the industrial revolution; others bought or maintained their country houses, and some used the money for philanthropy.