The Liverpudlian ¹ phrase where the bugs wear clogs has been used to characterise:
1-: An insalubrious place.
2-: A rough area.

¹ The adjective Liverpudlian means of, or relating to, Liverpool. Historically situated in Lancashire, a county of north-western England, Liverpool is a city and seaport at the east side of the mouth of the River Mersey.

1-: An insalubrious place:

The phrase is first recorded in Scouse Talks (1957) ², consisting of tape recordings made in Liverpool City Library with accompanying texts and ‘translations’—as quoted by Tony Crowley in The Liverpool English Dictionary: A Record of the Language of Liverpool 1850—2015 on Historical Principles (Liverpool: Liverpool University Press, 2017):

Some of the ould houses, bugs wid clogs on in um.
     in standard English:
Some of the old houses, bugs with clogs on in them.

² Scouse Talks was a project initiated and implemented by the Liverpudlian author and journalist Frank Shaw.

2-: A rough area:

The phrase where the bugs wear clogs has been used by Liverpudlians to characterise the neighbouring town of Bootle.

The following about Bootle is from County Borough Elections in England and Wales, 1919–1938: A Comparative Analysis – Volume 1: Barnsley – Bournemouth (Routledge, 1999), by Sam Davies and Bob Morley:

Bootle was situated on the banks of the River Mersey to the north of its much larger neighbour Liverpool. It had developed as a separate county borough from 1868, but in economic and social terms it had become an extension of the larger city well before the inter-war years.

The following amusing explanation is from “Talk Lancashire or Belt Up”, the BBC language handbook—as quoted by Miles Kington in All You Need to Know About the North, published in Pick of Punch (London: Punch Publications Limited in association with Hutchinson & Co (Publishers) Limited, 1970):

Bootle, where the bugs wear clogs.
A reference to the famous though long defunct Knowsley’s Bug Circus of Bootle. Sid Knowsley trained his clog-shod, chain-smoking troupe of performing bugs until they could re-enact any given dock strike, Liverpool-Everton ³ match or Saturday night function. He was forced to retire in 1933 after a disastrous Catholic/Protestant punch-up among the bugs. ⁴

³ Everton is a suburb of Liverpool.
⁴ Cf. ‘to pop one’s clogs’: meaning and early occurrences.

The earliest occurrence of the phrase where the bugs wear clogs that I have found is—in an extended form—from a letter by one Rol Fry, of Liverpool, published in the Liverpool Echo and Evening Express (Liverpool, Lancashire, England) of Monday 13^th March 1961:

Everton’s early Derby games were with Bootle, with a well deserved reputation for toughness not only on the field, and fist fights on the terraces were commonplace. Feet were definitely barred in those days. A derisive taunt was “Tricky Bootle, where the bugs wear clogs and fly backwards to keep the dust out of their eyes.”

The phrase where the bugs wear clogs occurs in Busy Bootle in the spotlight, by Ernest Dewhurst, published in The Guardian (Manchester, Lancashire, England) of Tuesday 4^th August 1970:

Developments costing £60 millions have added a new dimension in seven years to the former genteel watering place which later became known largely for docks and tanneries and a name which encouraged such jibes as “Brutal Bootle” and “Bootle where the bugs wear clogs.”

An extended form of the phrase occurs in Days of Hope (London: Headline Publishing Group, 2010), by Lyn Andrews:

‘You know what they say about Bootle?’
‘It’s where the bugs wear clogs and the kids play tick ⁵ with hatchets,’ Mags replied, using an old and derogatory saying that implied it was a very tough place indeed.

⁵ This probably refers to tig, denoting a children’s game in which in which one of the players pursues the others until he/she overtakes and touches one, who in his/her turn becomes the pursuer. The noun tig is a variant of tick, denoting a light but distinct touch.

According to the following from the Daily Mirror (London, England) of Wednesday 11^th September 1963, the English pop singer Billy J. Kramer (William Howard Ashton – born 1943) applied the phrase where the bugs wear clogs to Manchester, a city historically situated in Lancashire—“the boys” were The Dakotas, then Billy J. Kramer’s backing band:

It was Billy J., neatly turned-out with a button-down collar and very “sharp” suit, who sat opposite me yesterday on a London-bound train.
Like most of the leading lights in the “beat” groups pounding their way round Britain he is personable, polite, with that protruding quiff of hair that hallmarks every self-respecting “idol.”
“Our manager, Brian Epstein ⁶, makes it a rule, y’know, like we always have to look smart and behave ourselves,” he grinned. “But then me and the boys never did anything else. They come from Manchester—where the bugs wear clogs as they say, y’know.
“I come from Liverpool—started out as an apprentice fitter on the railways, never thought I’d end up travelling first class all round the country.”

⁶ The British businessman and music journalist Brian Epstein (1934-1967) was also the Beatles’ manager.