The British-English phrase the Ham and Egg Parade denoted a promenade at New Brighton, a seaside resort in Wallasey, Cheshire, in north-western England. The following explains the creation of New Brighton—source: History of Wallasey:

In 1830 James Atherton, a retired Liverpool merchant bought 170 acres of sandhills and heathland for a new settlement and watering place. He named it after the fashionable resort of Brighton. He had an ambitious plan for New Brighton which included rows of large villas, built one above the other, all with unimpaired sea view, for wealthy Liverpool merchants, grand hotels and a ferry. Some large villas were erected but a few years later a terrace of cheap lodging houses was built and a collection of low eating houses appeared. The wealthy merchants started to move away from New Brighton.

The phrase the Ham and Egg Parade alludes to the fact that cooked ham served with eggs was a popular dish at New Brighton’s eating-places—as explained in the caption to the following photograph, published in the Liverpool Echo and Liverpool Express (Liverpool, Lancashire, England) of Thursday 11^th August 1966:

The Ham and Egg Parade was a famous promenade at New Brighton, running from the Pier towards the present site of the open-air swimming pool. It was at its most popular at the turn of the century, and gained its nickname from the fact that two out of every three shops on the parade were eating-houses specialising in ham and eggs. The promenade was narrow and the buildings terraced, with shops at ground level and a pavement walk along the first storey giving access to the boarding houses above.

(Incidentally, it was at New Brighton that Bernard Pykett, a one-legged diver, coined the Liverpudlian phrase don’t forget the diver.)

The earliest occurrences of the phrase the Ham and Egg Parade that I have found are from The Birkenhead News and Wirral General Advertiser (Birkenhead, Cheshire, England):

1-: Of Saturday 12^th June 1880, in a letter to the Editor, by a person signing themself ‘Fairplay’, who criticised “a recommendation from the Works and Health Committee that Inspector Roach’s salary for his exertions in preserving order on the foreshore at New Brighton be increased to £30 per annum”:
—the phrase was already in common usage, since ‘Fairplay’ did not feel the need to explain it:

What good has the salary of £20 8s. paid in the past done? Has it lessened the countlese [sic] complaints which the inhabitants of New Brighton are constantly presenting to the Board? Has it stopped the disgraceful system of touting, which has so materially injured New Brighton as a sea-side resort? Has it lessened the dangers to which visitors are subject by the reckless galloping of horses and donkeys along the shore? or has it stopped the discordant soundings of the hordes of organ grinders and concertina players, which spoil the appetites of the patrons of the ham and egg parade? No, sir! far from it.

2-: Of Saturday 9^th April 1881, in the review of a theatrical farce titled Ici on Parle Francais:

The cast were all, with the exception of Victor Dubois (Mr. E. Escolme, of Birkenhead), district amateurs, and proved themselves of such calibre as to take us rather by surprise. The character of Spriggins, one of those grumbling, never-contented beings, from whom the New Brighton people pray for deliverance, was well delineated by Mr. Ernest Edwards, whilst we are sure that the Ham and Egg Parade could not produce a match for his estimable partner, Mrs. H. Sharpe.

3-: Of Saturday 7^th May 1881:

New Brighton.—The dawn of the season has appeared, yet withal, clouded by the intervention of three chilly or threatening days to one of sunshine. Be that as it may, the dependents upon pleasure seekers are brushing up, and, if we are to judge by the extension northwards of the Ham and Egg Parade, we would say with some prospect of success.