Kane marked the milestone in emphatic fashion on Tuesday, scoring twice and setting up another goal as England beat Czechia 3-0 at Wembley. The result moved Thomas Tuchel's side closer to securing their place in the Nations League quarter-finals.
"He is the best England player to ever wear the shirt and it is an honour to play with him," Bellingham said. "He is pretty unmatched. He is scoring goals for fun, he goes deep and he gets tackles in. He is only getting better."
The Real Madrid midfielder also praised Kane's character and influence away from the pitch, saying his achievements were a reflection of the work he puts in.
"He is an unbelievable human being, as a captain and a man," Bellingham added. "Everything he gets, he deserves. He works so hard for it, and he's a very honest guy."
Kane, who turned 33 earlier this year, now has 91 goals for England and will move clear of Shilton when he next features for his country. England are due to face Croatia next month, giving the striker an opportunity to become the outright record appearance holder.
His latest display underlined why he remains central to England's ambitions. Kane was involved in all three goals, with his cross leading to Vladimir Coufal putting through his own net before the Bayern Munich forward added two himself.
"It's right up there," Kane said of reaching 125 caps. "This is even beyond my wildest dreams. To be joint at 125 is an extreme privilege. I love coming to every England camp. Tonight was a special night."
Kane also made clear that his international career is far from over. After returning from what he described as his best season, he believes he can continue playing at the highest level for years to come.
"I still feel like I've got room to improve," he said. "I'm not going to stop. I'm going to keep pushing and see where it takes me."
The striker has previously said he would exchange his individual records for a major trophy with England, despite continuing to close in on the game's biggest international scoring milestones.
For Bellingham, meanwhile, the current England side is benefiting from spending more time together, with the midfielder forming part of an increasingly potent attack alongside Kane, Bukayo Saka and Anthony Gordon.
England have scored 12 goals without conceding against Czechia and Croatia during the current run, while also pushing world champions Spain before losing 3-2.
"I think with the longer camp, we have a chance to gel and bond and spend more time with each other," Bellingham said. "Eventually it shows on the pitch."
