Try this way,

use strict;
use warnings;
use Data::Dumper;


while(<DATA>)
{
    my @array = $_ =~ m/\b([A-Z]+(?:\d+)?)\b/g;

    print "@array\n";
}

__DATA__
BROUGHTON VETERINARY GROUP123. Leicestershire mixed practice seeks exp
+erienced vet to replace assistant relocating to Scotland
GIRLING AND BOWDITCH VETERINARY SURGEONS We are looking for an experie
+nced vet for our 5 vet mixed practice.
STANHOPE PARK VETERINARY HOSPITAL. Due to a pregnancy epidemic we are 
+looking for 2 new vets, 100% small animal hospital in County Durham.
[download]

What about capitalized words later in the line? Shall they be excluded?

use strict;
use warnings;

while(<DATA>)
{
    my @array = $_ =~ m/\b([a-zA-Z]+[0-9]*)\b/g;
    foreach (@array) {
        last if /[a-z]/;
        print "$_ ";
    }
    print "\n";
}

__DATA__
BROUGHTON VETERINARY GROUP123. Leicestershire mixed practice seek EXPE
+RIENCED vet to replace assistant relocating to Scotland
GIRLING AND BOWDITCH VETERINARY SURGEONS We are looking for an experie
+nced vet for our 5 vet mixed practice.
STANHOPE PARK VETERINARY HOSPITAL. Due to a pregnancy epidemic we are 
+looking for 2 new vets, 100% small animal hospital in County Durham.
[download]

Thx. Vinoth