Given that you were offered, and have started the job, I think it is unlikely that this omission will cause you any problems in your current job. At the interview stage someone might conceivably care, but once you have started, particularly as a junior (and young) employee I very much doubt that anyone is concerned with either background checking you or indeed in thinking about your past history at all. If I were in your shoes I would not confess at this point as the negative impact is guaranteed in that course of action, but only possible if you say nothing.
However, there may well be tax implications - If you were employed and PAYE in your prior job then you will have a tax position- you will be on their radar. When you left your prior employment they should have provided a P45 that is then given to your new employer and used to restart your tax affairs for the new position. If you didn't provide your new employer a P45 then they will not take your prior earnings into account and will report a position to the tax office that will differ from what they have on their records. This may or may not surface at some point.
If you were only at your prior employer for a short period they might have just written you off and perhaps you didn't accrue any taxtaxable income, and hence they didn't issue a P45 - In other words, perhaps according to the tax office it is as if you had never worked, in which case all will be well.
But if it isn't like that then you may have an issue. If you ever received a payslip that showed you had paid tax, or you received a P45 and/or a P60, then the tax office will have a record of your tax position.
Whether you choose to do anything about this, or take the view that you will plead ignorance of the complications of tax if it comes to light, or some other coping strategy, is up to you and this is probably not something the internet can or should advise you on.