Your amp should be enough for that speaker, it's the speaker itself that is maybe not strong enough, and combined with a low input signal from your phone, it won't get loud.
The cheapest would be the Wiim amp mentioned above (and it's also a better amp than the peachtree) as it gives a better input and has almost double the wattage, but better (I mean mostly louder) speakers would also be great to solve this. You want 105dB peak/85dB RMS minimum in your living room at the listening distance to go loud, You now get way less.
And also, that Kef is not a very good speaker, it's cheap, also in design with a very simple 1st order crossover and a not so good designed cabinet so it has a lot of unwanted resonances that i can hear at least. It's not something like the R3 or the LS50 that are way better designed by Kef. I never saw measurements of it, but i'm quiet sure Amir (or Erin) would find a lot wrong with this one when they would measure it.