Does the price movement of gold in my TallyMoney account trigger capital gains tax?

No, a capital gain/loss is only realised at the point in time when you spend or send your tally (i.e. sell or dispose of an asset). Furthermore, all transactions throughout a tax year and the capital gain/loss incurred with each transaction can only be aggregated to calculate CGT, at the end of a tax year. 

Any change in the GBP value of your tally balance in your TallyMoney account is “unrealised” and not subject to calculation for CGT purposes.