It looks like a lenticular cloud but also like a saucer. Pretty cool how it sticks around like it does.
(https://i.imgur.com/12u66Zd.jpg)
(https://i.imgur.com/DIePelN.jpg)
https://www.youtube.com/watch?v=aVvDsGP9hPg
https://www.youtube.com/watch?v=zvG2PJUMv5A
It does look like a lenticular cloud, but those clouds are formed when the wind finds an obstacle, usually a mountain or a hill, but I don't see any of those things in that area, not even a tall building.
As far as I am aware / recall.. Parts of South Yorkshire around Barnsely in the UK ..does have some higher hill or mountain areas...
In the ref to the image or video thou...
I do find it interesting and have seen similar things before... both for real and on several UFO type TV programs..
I suspect that it is a cloud...but will say that it does look like a Mothership...
I have not studied the videos on much detail at this stage... but so far on a quick browse..
What I have noted depending on where the cameraman was taking the film from....is that the object slowly seems to move up higher as the video moves on in ref to a certain part of the house roof..
see at 1 min 54 secs how it compares to the top of the house roof ,to the position that it was to the roof top at the start of the video... (I later noted the images posted do show this difference of the position in relation to the roof of the house)
so i assume that the object is moving up some how and maybe coming also towards the house..and not going further away from it.
Would a cloud do that ? on what seems like calm conditions..
Often at or towards sunset times.. you see clouds appear to move lower or disappear..
but maybe depending on wind directions / atmospheric conditions.. maybe the wind slowly moving the object or cloud to move more upwards and towards the house..
unless the cameraman has moved to another vantage point or position that alters the angle that he is able to film the object from..
He did refer to having seen the object for over an hour in the 1st video..
but what we see on the video .. is about 4 to 5 mins worth... BUT that footage may not be continuous footage... it maybe just clips every now and then say over an hour or so... that would make the movement of the object appear to have moved a fare way in 5 minutes... but in relality that may have taken an hour or so..
if it has moved up within a few minutes.. that i would be quite surprised that a cloud would move that far in that time frame unless there was a stronger aircurrents or winds to move it so... which if there was string winds... I may question would the cloud remain in that same shape for so long..
I THINK on the day it was said to be filmed in the UK in general that day.. June 28th... Conditions were quite calm around most of the Country.. at least where I live I think that they were....
but there may have been some parts of the country that did have slightly different conditions and maybe even windy on the eatern side which is where Yorkshire is..
But the next day on the 29th.. we may have some wind gusts occur
looking at the enlarged 2nd and 3rd image.... on the extreme right and left edges.. the object shape seems to have altered slightly... that may suggest its an alteration in the clouds shape..if its slowly changing position as it has moved or breaking up slightly for eg..
In the 2nd video... he seems to have moved to another nearby position a bit later in the same day as its going darker..
but he later moves back in sight of the house.. so he did not seem to move very far away from the 1st video vantage point..
It would take some further study and trying to analyse the vdeos more and what he may be saying to try to determine it better..
On looking at video 1 again... I did not realise that initially he was inside his house at the beginning, later then he went outside...
at 1 min 12 to 16 secs..... I noted a series of small lights on the tree to the right side of the house.. and a slight appearence of something above the object...that looked like a bit of a reflection and a slightly lighter image of the object..
is the a camera reflection or something ? on the window ???
Maybe when he then goes outside... if he stepped down lower.. or stepped up... maybe that altered the position of the object in relation to the house roof top..
at the 3 min mark the object is slighly above the top flat roof.. (not the chimney)
but later I also noted the object go back down a bit back or level or slighly below the house roof top..also in the 1st video .when he had moved the camera and then came back at the 3 min 16 sec mark...