This is what IGC have on them:

Name Edward & George Higham
Other Names E & G Higham
Address1 9 Ranelagh Street
Address2 4 Adelaide Buildings, 4 Chapel Street
City/Town Liverpool
County Lancashire
Country United Kingdom
Trade Gun makers
Dates 1857-1920?

Notes

Edward Higham (b.1833) and George Higham (b.1834 George (II)) were the sons of George (I) and Mary Higham of Warrington. They were recorded in the 1851 census, aged 18 and 17 years, living with their parents in Horse Market Street, Warrington, along with their younger brother, Stanley (b.1846). Both Edward and George were described as gun makers and worked for their father.
In 1857 they moved to Liverpool where they established their own business at 9 Ranelagh Street, next door to William Dooley at 11 Ranelagh Street, with additional premises at 32 Berry Street. William Dooley was born in Warrington and may well have been apprenticed to the Higham family of gun makers, he may have been related to them. In 1858 William moved his business from 11 Ranelagh Street to share the Higham's premises at 9 Ranelagh Street. The 1861 census records Edward married to Elizabeth (b.1834 in Warrington) and living at 51 Upper Hope Place with a daughter, Mary E (b.1861). George lived with them. Edward described himself as a gun maker employing 1 boy. In 1865 William Dooley, aged 62, sold his business to Edward and George. In the 1871 census Edward and Elizabeth were recorded living at 9 Ranelagh Street with another daughter Patty (b.1864). George still lived with the family and Mary, Edward's mother was staying with them on the night of the census. She was described as a gun maker and farmer of 35 acres employing 2 men.

No record of the family has been found in the 1881 census. Stanley had taken over the Warrington business from his parents, George and Mary, in the 1860s, and in the 1871 census was recorded at 19 Horse Market as a gun maker (see George Higham of Warrington). However, by the time of the 1891 census he was manager of the Conservative Club in Warrington and by 1901 was an employed gun maker in Folkestone, Kent. He may have gone to the south coast of England for the sake of his health, but he died in Ulveston (overlooking Morecombe Bay) in Lancashire, in 1925. The 1901 census records George as a 67 year old gun maker and farmer living at Sandringham Farm, Birkdale, Southport (about 25 miles north of Liverpool) with Patty and Fanny, and Stanley George Higham who was Stanley's son and George's nephew. Stanley George was described as a gunmaker's manager, almost certainly managing the business in Liverpool for Edward and George. Edward was also recorded in the census but separately, he was a widower, gun maker and farmer at Hill Side, Sandringham Farm. The census records George, Patty and Fanny (b.1872 in Liverpool) living with him. It also records that on the night of the census Eleanor (b.1872 in Warrington) who was the Stanley Higham's daughter, was staying with them. In about 1905 the firm moved to 4 Adelaide Buildings, 4 Chapel Street.

In about 1920, the business was sold to W C Carswell.

Other Info
The firm sold "Gastight & Metal Lined" shotgun cartridges under their own name.

Since you may wish to know about Carswell too, this is what IGC have on them:

Name William C Carswell
Other Names W C Carswell Ltd
Address1 E1 & F2 Exchange Buildings, Chapel Street
Address2 4 Chapel Street
Address3 19 Old Hall Street
City/Town Liverpool
Country United Kingdom
Trade Gun & rifle maker
Other Address
Dates 1913?-1982

Notes

William C Carswell established his business in about 1913 at E1 and F2 Exchange Buildings Liverpool. In about 1920 the firm bought the businesses of Hooton & Jones and E & G Higham, they gave the latter's address at 4 Chapel Street as their principal trading address. In about 1935 the firm became a limited company, W C Carswell Ltd. In about 1960 the company moved to 19 Old Hall Street. They ceased to trade in 1982.
Other Info
The firm sold cartridges under the names "Carswell's Special" (post 1922) and "Banshee" (1920?-1960).

Tim