Last month the Home Office redeployed hundreds of staff to deal with a backlog of 30,000 applications, but some people are still experiencing delays putting holidays and trips abroad in jeopardy.
14-year-old Megan Richards from Newport is one of thousands of people affected by yesterday's strike.
Megan's grandmother Christine Richards said they had to travel to Peterborough.
"This is the first appointment we could get. We couldn't get one in Newport at all. The people have a right to strike... but when it impacts on you personally it's sometimes a little bit difficult to be sympathetic."
A spokesperson for the Home Office said the strike was 'irresponsible' and will lead to further inconvenience for customers.
The Public & Commercial Services union says that more than five thousand Welsh civil servants will strike today. The action is part of the union's campaign against government cuts.
Those involved tomorrow will include workers in the DVLA in Swansea, Companies House in Cardiff, the Intellectual Property Office in Newport and the Land Registry in Swansea.
Next Thursday, 6 June, will see a one-day strike throughout Wales by PCS members in the Department for Work and Pensions and HM Revenue and Customs, while National Museum Wales workers will be striking on Saturday, 8 June.
"We are low paid workers. We've had a pay freeze for two years" says Dave Warren, from the PCS union.
"This year, there's a one percent increase available, which is a joke in itself, but apparently the Government wants to tie that to the loss of our terms and conditions. We find that totally unacceptable."
Several transport offices will be affected today as workers for the Department for Transport take strike action over pay and conditions.
DVLA offices in Swansea, Bangor and Cardiff
The DfT Shared Service Centre in Swansea
Maritime & Coastguard Agency staff in Swansea, Holyhead and Milford Haven
Vehicle & Operator Services Agency staff at the agency's office in Swansea and goods vehicle testing stations around Wales
Driving Standards Agency staff at driving test centres and an administrative office in Cardiff.
Llanishen Tax Office
In the lead up to industrial action Cabinet Minister Francis Maude suggested rather than take strike action and lose pay we could just take 15 minutes out to protest. This November 30th we are taking him at his word and organising such a protest in our workplaces.
– Malcolm Degroot, the Public and Commercial Services Union
Around 4,000 Welsh staff who work for the Department for Transport will go on strike in Wales today. It follows a long running dispute between workers and the DfT over pay, job losses and closures of offices.
A letter will be addressed to the Welsh Secretary, David Jones, urging him to stand up for the interests of civil servants in Wales. The Public & Commercial Services union says that the letter cites attacks on pensions, pay and terms and conditions.
Of particular focus will be the threat of regional pay which the union claims is set to hit Wales harder.
It also states that: "If Mr Jones takes seriously his role as Wales' voice at the Cabinet table, he should seek to persuade his ministerial colleagues to halt and reverse the cuts, before irreparable damage is done to public services in Wales and throughout the UK."
In total, around 4,500 employees outside of Wales will be taking part in protests across the country.