The defensive pair, who were both snapped up by boss John Still this week, are confident Hatters can take League Two by storm after winning the Conference title last term.
On trying to get out of the division at the first attempt, Wilkinson, who was signed for an undisclosed fee from Still’s former club Dagenham & Redbridge, said: “Definitely, that’s the way it should be, we should be looking to get promoted again.
“A lot of people might say, we’ve just come up, we should consolidate in League Two, but there’s a lot of ambitious people at the football club.”
Connolly, who has extensive Championship experience with Plymouth, Derby, Sheffield United and Leeds, believes there is no reason he can’t be at that level again while with Town.
The 30-year-old full back said: “This club has got potential to be in the Championship.
“It should be in the Championship but it’s not, so the gaffer is trying to rectify that.”
Their views were echoed by another recent addition in striker Ricky Miller, who is confident Town can continue the success shown by other Conference champions.
He added: “There’s no point aiming for mid-table or aiming to escape relegation because the squad that we’ve got there’s more than enough quality in there to challenge.”
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