What is the op-amp in this JFET-matcher circuit?
As Brian says, pretty much any opamp that can operate with a total supply voltage of 9V or less (i.e., NOT a 741!) will do the job. It's used at DC and unless you care about the last mV of mismatch, its input offset voltage and current won't upset the match very much.

To address your additional concerns:


  Can I build the matcher on a breadboard or will it be better to solder together?


It doesn't much matter. If it's something you'll be doing fairly often, you'll want to pick a sturdier construction technique.


  Given the purpose of the circuit I'm matching the JFETs for (eg. it's run off 48V phantom power, not a 9V battery) should I make any adjustments to the matching circuit (ie. use a voltage source other than 9V battery; a different Rset value)?


The circuit sets the JFET up as a current source. Increasing the voltage will simply force it to dissipate more power and change its temperature, possibly confusing your results. With this in mind, you do want the transistors to be best matched under the same conditions under which they'll be operating in the actual application, so use your own judgement.


  Or can anyone recommend a matched JFET component available in the UK?


Product recommendations are off-topic here.