For minor damage by fire, the sentencing guideline is from a medium level community order up to 12 weeks custody. (See page 23):
https://www.sentencingcouncil.org.uk/wp-content/uploads/MCSG_web_-_October_2014.pdf
However those sentences are for a first-time offender who has pleaded 'not guilty'. A reduction in the sentence is available for a guilty plea.
If the burglary was in domestic premises and regarded as being at the bottom of the scale (with both 'culpability' and 'harm' being categorised as 'low') the sentencing range runs between a low level community order and 26 weeks custody. (See page 217 in my link).
Given that the 'starting point' sentence for both offences is a non-custodial community order, I'd guess that would be the most likely outcome. (e.g. 150 hours unpaid work, plus costs, compensation and a £25 'victim surcharge').
However my response assumes that the lowest category is used for sentencing the burglary offence. If there's any reason for a higher classification to be used (e.g. high value items stolen and not recovered) a custodial sentence would be far more likely.