Harry Redknapp hailed Gareth Bale as one of the best players in the country after Tottenham Hotspur turned up the heat on Manchester City and Manchester United, the top two in the Premier League, with a stirring 2-0 victory over Norwich City here on Tuesday night.

Third-placed Tottenham narrowed the gap to the Mancunian pair to seven points – and the north London club have one game in hand over them – thanks to the pace, power and precise finishing of Bale. In a magnificent solo display he scored twice in the second half to snuff out Norwich's brave challenge.

But when the transfer window opens next week Redknapp is adamant that he will fight tooth and nail to ward off any potential suitors of the Wales winger. "Is Gareth the best in the country? Well, he is some player," Redknapp said. "He's an amazing player, sometimes unstoppable. And the thing is, he's a great lad as well.

"There's nothing flash about him, that's just not him. He's no Billy Bighead. He just comes in, he loves to train and just gets on with it. No, of course, we're not going to sell him. If we do that, we've had it. And anyway there's only Barcelona, Real Madrid or Manchester City who could afford the fee and wages."

Bale had to endure unpleasant chanting about his looks from fans in the notorious "Snakepit" section of the crowd, especially in the first half as he played towards them. It provoked a scathing reaction from Redknapp. "That was disrespectful," he said. "I don't even want to talk about it. It makes you sick."

Not one to respond to the abuse, Bale simply punished Norwich with his two second-half strikes. "We've learned a lot from last season, being in the Champions League," he said. "We've added a few new players, which has improved the team, and I feel that I'm improving all the time. And so is the team.

"From last season in the Champions League we have learnt from the big teams – playing against them and how they play. We have adapted that style in a way. We try to be patient but we know we are going to create a lot of chances with the players we've got. We were patient tonight and we got our goals to win the game.

"It was a great weekend for us. The gaffer said before the game that a lot of results had gone for us this weekend and it was a big opportunity for us to take advantage of that. We did that, which was important – to put pressure on the teams below us and above us."

Bale's double – he has scored six goals in eight league games – enabled Tottenham not only to put the pressure on City and United but also to stretch their advantages over Chelsea and Arsenal, their London rivals. Chelsea lie four points adrift of them and Arsenal five, with both having played a game more.

Tottenham also have a potentially straightforward run of fixtures coming up, with four of their next six matches at White Hart Lane – against West Bromwich Albion, Everton, Wolverhampton Wanderers and Wigan Athletic. Next up is a trip to South Wales to take on Swansea City on Saturday and they have to take on Manchester City at the Etihad Stadium on 22 January.

But if there would appear to be rich pickings to be had at the Lane, Redknapp urged caution. "Sure, the results went well for us this weekend but we still had to make full use of that," he said. "Others may have dropped points but it just shows how everyone is scrapping for their lives.

"OK, you might look at some [easier] games and you might think 'Yeah, yeah'. But it's so hard to pick up good results these days. Just look at Liverpool. Who'd have thought that they would fail to beat Blackburn at Anfield? We don't worry about the opposition. We just go out to win games.

"I still think that the two Manchester teams are favourites for the title. United look really strong to me. You can't write them off, can you? We'll just keep doing our best, keep winning games and see where that takes us."