Victoria
The main reason the population in the industrial districts/ towns like Manchester 'vastly' increased was because people moved in from the surrounding Lancashire, Yorkshire, Cheshire etc countryside. Though most people attending Peterloo were not actually from Manchester. They came from surrounding town's
Yes there were waves of Irish immigration at certain times, circa late 1840s, circa 1900 and also after the last war, but the Irish joined a huge demographic of English Working Class and so did not make a 'vast' difference to the population and especially not in 1819.
These are the most common surnames in Lancashire in 1881. The surnames for Manchester, even now, are similar
http://www.britishsurnames.co.uk/1881census/lancashireSMITH 45,465 1.3115 0.93
TAYLOR 38,342 1.1060 1.73
JONES 34,724 1.0017 0.88
JACKSON 18,242 0.5262 1.88
WILLIAMS 18,213 0.5254 0.73
BROWN 17,335 0.5001 0.76
ROBINSON 16,378 0.4725 1.48
WILSON 15,643 0.4512 0.98
JOHNSON 15,078 0.4350 1.29
ROBERTS 14,387 0.4150 1.10
HARRISON 13,369 0.3857 1.74
DAVIES 13,293 0.3835 0.75
THOMPSON 13,089 0.3776 1.26
WOOD 13,015 0.3754 1.18
HUGHES 12,467 0.3596 1.28
WALKER 12,032 0.3471 1.04
HALL 11,757 0.3392 1.15
SHAW 11,616 0.3351 1.82
TURNER 11,591 0.3344 1.20
HOWARTH 11,395 0.3287 6.84
HOLT 10,528 0.3037 4.54
WRIGHT 10,502 0.3029 0.94
GREEN 10,442 0.3012 1.07
WILKINSON 10,296 0.2970 1.95
ASHWORTH 9,551 0.2755 6.91
EVANS 9,220 0.2660 0.61
YATES 9,171 0.2646 3.85
HOLDEN 9,076 0.2618 4.78
MORRIS 8,723 0.2516 1.13
RILEY 8,663 0.2499 3.16
KELLY 8,522 0.2458 2.24
WALSH 8,416 0.2428 4.56
BOOTH 8,397 0.2422 2.46
LORD 8,273 0.2386 5.18
WHITTAKER 8,043 0.2320 4.90
SCHOFIELD 7,978 0.2301 4.25
BUTTERWORTH 7,951 0.2294 6.39
HARGREAVES 7,874 0.2271 5.45
PARKINSON 7,744 0.2234 4.66
CHADWICK 7,697 0.2220 5.08
HILL 7,522 0.2170 0.85
HARTLEY 7,518 0.2169 3.46
LEE 7,497 0.2163 1.32
GREENWOOD 7,302 0.2106 2.71
WHITEHEAD 7,269 0.2097 3.10
KAY 7,249 0.2091 4.02
WARD 7,223 0.2084 0.95
FLETCHER 7,205 0.2078 1.82
EDWARDS 7,112 0.2052 0.74
BARNES 6,968 0.2010 1.67