Spot the difference:
• ‘The British will likely complain about how Americans use English’;
• ‘It is likely that the British will complain about how Americans use English’.
It’s certainly true that the British often whine about American usage, but it has to be conceded that the two sentences above are clearly different, grammatically speaking. In the former, ‘likely’ is adverbial, and in the latter, it is adjectival.
Increasingly, Brits are using ‘likely’ in the former way as a mid-position adverb that has a meaning akin to ‘probably’ or ‘possibly’. It is associated with American English, but in the UK you can now find it everywhere.
However, this usage is neither right nor wrong, just different. It may also be incorrect to suggest that the adverbial form associated with American English is, in fact, American in the first place – some commentators have found examples of it in use in 14th-century English.
Indeed, what matters here is the intended meaning: both sentences above convey the same sentiment, more or less.
Which means that at the end of day the use of ‘likely’ is simply a matter of style and preference. Probably.