It can. A bridging loan is a credit commitment, so it will normally appear on credit records and will be taken into account when a lender assesses affordability. Some mortgage lenders are entirely comfortable with a bridge that has a clear exit; others treat it as a reason to look more closely.
The effect depends on context. Where the bridge is being repaid by the mortgage you are applying for, it is usually part of a planned sequence and lenders expect to see it. Where it is unrelated borrowing that will continue alongside the mortgage, it reduces the amount you can afford to service.
Conduct matters most. Missed payments, an extension beyond the original term, or a default will show and can be damaging to a later application. Rolled-up interest that has grown the balance may also change how the debt is viewed.
Applications and searches leave a footprint too. Several credit applications close together can prompt questions, so plan the order in which you apply.
Be open about any bridging with your mortgage adviser or lender from the start. Non-disclosure discovered later is far more harmful than the borrowing itself.