This group of twenty-three men are on an excursion somewhere, presumably somewhere near West Hartlepool (Durham), as that is where the photographer is from. Roughly half of them are bearded, and most of the remainder have moustaches and sideburns or Dundreary whiskers - only one young man, possibly in his mid-twenties clearly has neither. Many have bowler or homburg hats, although they have taken them off for the portrait. One has an umbrella and at least a couple have walking sticks.
Unfortunately I'm not familiar with Durham and the area around West Hartlepool at all, so I can't begin to suggest where it might be located. However, it may be that the cliff backdrop to the photograph immediately suggests a spot to someone with local knowledge - if so, I'd be pleased to hear from you (Email). I think it was taken in the late 1880s or early 1890s but, as I'm not particularly adept at dating men's clothing fashions, I'm quite likely to be out by a few years either way.
The photographer Robert Leithead was primarily a chemist, druggist and proprietor of a hairdresser's salon, who appears to have carried on the photography as a sideline, perhaps only briefly, styling himself as "Lew." An 1890 trade directory (Kelly's Directory of Durham, courtesy of the University of Leicester's Historical Directories) shows him with a chemist's shop at 58 Milton Street, and a hairdressing shop in Murray Street, both in West Hartlepool. The 1891 Census suggests that he was also a wine merchant and photographer, and that his fifteen year-old daughter Isabella was working in the hairdresser's as a "shop woman."
Photo-Sleuth reader and contributer Nigel Aspdin has come up with a possible location for this photograph.
Maybe it could be High Force Waterfalls, which is further inland up the Tees, but it would be a day out trip from West Hartlepool. The Tees goes through Co Durham and exits into the North Sea at Hartlepool. We were there a few years ago but for some reason I have no photos of the falls, just [a photo outside the pub] at the top of the long path back up to the car park! If it was High Force, and I do think it quite likely, then I am sure your men had a pint or two at the same pub.According to a Wikipedia article High Force is a waterfall on the River Tees, near Middleton-in-Teesdale, and was formed where the river crosses the Whin Sill: "The waterfall itself consists of two different types of rock. The upper band is made up of whinstone, a hard rock which the waterfall takes a lot of time to erode. The lower section is made up of carboniferous limestone, a softer rock which is more easily worn away by the waterfall. The wearing away of rock means that the waterfall is slowly moving upstream, leaving a narrow, deep gorge in front of it."
High Force waterfall, near Middleton-in-Teesdale, Tees Valley
Image courtesy of Wikipedia & Adrian Barnett/StoatBringer
Modern photos of High Force, such as this collection from Pictures of England, do show rock faces which are very similar to that in the background of Leithead's group portrait. It may even have been taken close to the lower right of this recent photo by Ben Gamble.
The spot is also shown on this satellite image from GoogleMaps:
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Ian West shows that the site is of some interest to geologists on his web site devoted to the Geology of Great Britain, hosted by the University of Southampton. It occurred to me that the group might be engaged on a geological excursion, but I think this is unlikely, as none are carrying hammers of any sort. A geological map of Durham on the same site shows that magnesian limestones outcrop for some distance to the north, west and south-west of West Hartlepool. Nigel and I are both of the opinion that the rocky outcrop in the background of the Leithead photo is probably composed of some kind of limestone. If this is the case, then it is still possible for the location to be closer to West Hartlepool than High Force, which has a dolerite sill overlying limestones and indurated shales, as shown in the portion of the geological map below.