Jim Dixon:
A good start, I've been listening as well, and can add/correct some.
Others please feel free to correct me in turn!

[Slow tempo at first:]
Well, I've been ev'rywhere.

I was drivin' my minimotor way down by the sea
When a scruffy-lookin' hitchhiker thumbed a lift from me.
I said, "Hop up inside, boy. Where you plan to go from there?"
He says, "I don't give a continental, castle boy (?), 'cause I've been ev'rywhere."

[Speeding up:]
One, two, one two three four.

CHORUS: I've been ev'rywhere, man.
I've been ev'rywhere, man.
Never a trouble or care, man.
I've never paid me fare, man,
And of travel I've had me share, man.
I've been ev'rywhere.

1. Been to Bradford, Guildford, Dartford, Littlehampton,
Bedford, Chingford, Hereford, Wolverhampton,
Shrewsbury, Canterbury, Aylesbury, Liverpool,
Scunthorpe, Sandthorpe??,Mablethorpe, Hartlepool
Whitehall, Bramhall, Mildenhall, Davenport
Newport, Southport, Stockport, "Hi Sport!". CHORUS

2. Been to Farnborough, Edinburgh, Peterborough, Petersham,
Middlesborough, Loughborough, Scarborough, Walthamstow,
..., ..., ..., l...,
..., ..., Hounslow, Tipperary
Hempstead, Wanstead, ...stead, Woodstock,
B..., ..., ..., "Watcha Cock!". CHORUS

SPOKEN: Change Gear. (sound effect of manual gear change)

3. Been to Weymouth, Yarmouth, Bournemouth, Huddersfield,
Lewisham, Faversham, Portesham, Sheffield,
Land's End, Mile End, Southend, Birkenhead,
Birmingham, Nottingham, Gillingham, Holyhead,
Cambridge, Tonbridge, Knightsbridge, ...,
Edgware, Brockweir, Carstairs, "Who cares?" CHORUS

4. SLOWLY, HESITATINGLY: I've been—to—hey, this is difficult!—I've been to—
Llandudno, Llanelli, Llanfairpwllgwyngyllgogerychwyrndrobwll. . . (fails before completing this place name!)
SPOKEN: No, it's no use. I'll never get those Scottish place names in a million years. Let's get back to the English version.

5. BACK TO FAST TEMPO: I've been to Westminster, Southminster, Kidderminster, Accrington,
Eastbourne, Southbourne, Sittingbourne, Paddington,
Bolton, Paignton, Stockton, Inverness,
Renwick, Brunswick, Chiswick, Dungeness
Mansfield, Sheffield, Enfield, ...,
..., ..., ..., .... CHORUS

I've been here, there, ev'rywhere.
I've been ev'rywhere.

It appears that each verse ends with a comment, "Hi Sport", "Watcha Cock", "Who Cares", which may confuse those only looking for place names

CHEERS

Nigel