There's talk of increasing the blocksize - if this can be achieved - does this mean that the 21m btc limit can also be changed? My understanding of the blocksize debate is that it would require 51% consensus to change the algorithm and accept the new blocksize. 

If the algorithm can be changed like this - would the exact same mechanism allow miners to also change the limit of bitcoin? 

Or is there something fundamental that prevents this?
Flat-out increasing the blocksize is a hardfork. Hardforks require the overwhelming support of all parts of the Bitcoin sphere to be adopted, otherwise they will create a forkcoin. 51% would be unlikely to suffice to implement a hardfork.

Changing the reward schedule and thus the Bitcoin supply would also require a hardfork. From a technical perspective, changing the reward schedule would probably require a similar level of changes in Bitcoin software to be rolled out.
However, getting support for a change in the Bitcoin supply would be much more difficult as it's a key precept of what Bitcoin is, while the blocksize is "merely" an operational value that has implications for the network's security and how the Bitcoin project develops. I therefore consider it extremely unlikely that the Bitcoin supply will change in the future, while a blocksize increase is almost certain.