Frederick Walker 1888-1954 Wellingborough event? Northants

[PalmTree1]

Bassett's Close makes sense to me too, though I still cannot picture it right, as in my younger days it was the location of the annual Charity Fete.

[ValJJJ]

I think there's too much open space there for it to be Swanspool Gardens, but IF it is Wellingborough, it could be Bassett's Close.
The fall of the land towards Northampton Road is similar, and there are/were large buildings along that road. The line of conifers has changed.
This may have been taken in a similar position to where the bandstand is now ... it was built in 1912. The tree close behind the performers is just like those in pictures from 1908.

I'd suggest you get on to Wellingborough Museum and ask their advice. Although closed at the moment, they do have a Facebook page and you'll find their email address on the Wellingborough Council's website at  http://www.wellingborough.gov.uk/info/200070/museums_and_galleries/844/wellingborough_museum

I contacted the museum and had an instant answer!  The person said a pierrot group wore white costumes, so not sure what this group was.  Also suggested posting the photo on the Wellingborough Then and Now Facebook page for more ideas.  I'll let you know.