This film consists of three separate parts, which the British Film Institute (BFI) lists as three different films: Leeds -  Street Scenes near Bridge, 1903; Street Scene in Boar Lane (Leeds), 1898; and Leeds - Views From Moving Tram (1903) - which is the order they are shown in here.  The 1898 film, Street Scene in Boar Lane (Leeds), is almost certainly to be by the Riley Brothers of Bradford - it is mentioned in the December supplement to the catalogue of the Warwick Trading Company of 1898 - where it is described as, "One of the best English street scenes ever exhibited. Passing trams, carriages, drays, &c. Full of animation. (75 or 50 feet)".  It also comes under the title of 'Peter Papworth Collection No. 7'; and it may exist in a separate version (see the online database of The City of the Future project, References).

Leeds - Views From Moving Tram might be a Mitchell and Kenyon title, given that they made at least three similar ones in Yorkshire: in Sheffield, and in 1902, in Halifax and Bradford (see Patrick Keiller, 'Tram Rides and Other Virtual Landscapes').  From 1898 through the 1900s many filmmakers made what are called 'phantom ride' films, usually taken from trains or a moving tram - on either the first and second deck - of the surrounding streets (the first such film was made in the USA in 1887, and they were popular also in France).  However, the phantom films made by Mitchell and Kenyon tend to be shot to the side, concentrating on the sidewalks, rather than straight ahead, as in this film.  Another feature of the Mitchell and Kenyon films is that they would often actively manipulate people on the sidelines - again, something entirely absent in this case.  Also, it does seem a coincidence that Views From Moving Tram begins at exactly the same place as Street Scene In Boar Lane, although there are some visual clues that it wasn't filmed at the same time.  

One of the interesting aspects of 'phantom ride' films, noted by Patrick Keiller, is that they don't direct the viewers attention to any particular part, in the way that modern films usually do.  Patrick Keiller used this feature in his own film The City of the Future, produced in 2007.

At this early stage films were often what are known as 'actuality films', showing local people and places.  These films were commissioned, and sometimes produced, by those working in the existing working class entertainment industry, to be shown in music halls, fairgrounds and public halls - either on their own or as part of a programme of other entertainment.  Often they would be shown on the evening that they were filmed: the film show would be advertised during the filming, using flyers and other forms of publicity.  In this way thousands could see themselves and their local towns or workplaces.  Workers leaving factory gates, or crowds at football matches, were filmed for this purpose.  There was a class differentiation here, with the working class preferring to see themselves - though the novelty of this gradually died off - whilst the middle class preferred ceremonial events (they also paid a premium for seats that avoided contact with the working class audience).

Another factor that casts doubt on the authorship is the quality of the film: this doesn't quite match those of the Mitchell and Kenyon films that have survived.  One reason for this may have been in the equipment used.  There were several different cine cameras around at this time, but it would be a fair guess that the middle section of film was made using the Riley Brother's own Kineoptoscope camera that they developed themselves in 1897, using an original patent from Cecil Wray, another Bradford filmmaker.    

However, information on these films is very scant - catalogues of the Riley Brothers have yet to be found - and so dating is somewhat speculative.  The acquisition of Leeds -  Street Scenes near Bridge and Leeds - Views From Moving Tram by the BFI - set up in 1935, and at that time called the National Film Archive -  is somewhat curious.  They were donated in two halves by the same pair of donors: half of each film arriving in 1936, the other half of both films arriving in 1946, and then put together some time in the 1950s.

The tram shown in the film travels from City Square along Boar Lane until the junction with Briggate, which is in sight, with the church on the left.  The shop on the corner, on the far side of Boar Lane near the start, is of L & NW Railway, with destinations in white lettering on the window (including 'North and South Wales', 'Blackpool', 'Wolverhampton').  The film features both horse drawn trams - started in Leeds in 1871 - and electric trams, as seen in this film.  Leeds was the first city to have an overhead electric tramway system when in 1891 it opened the Sheepcar-Roundhay route, extended to Kirkstall Abbey in 1897.

References

John Barnes, Pioneers of the British Film, University of Exeter, 1996.
Robert Benfield, Bijou Kinema, A History of Cinema in Yorkshire, Sheffield City Polytechnic, 1976.
Patrick Keiller, ‘Tram Rides and Other Virtual Landscapes’, in Toulmin, V, Popple, S and Russell, P (eds), The Lost World of Mitchell and Kenyon, BFI, London, 2004.
J.R. Thackrah,  Victorian Yorkshire, Dalesman Books, 1979.
Online database of The City of the Future project: