Wirex is part of the BitGo Instant network. This means you can send bitcoins to Wirex accounts from another Wirex account instantly (off-chain). This instant transfers feature will also work for funds transferred from other bitcoin wallets that are part of the BitGo Instant network.
For on-chain transactions outside of BitGo Instant network, the bitcoins sent to a Wirex account might take up to 30 minutes as we require 3 confirmations from the blockchain. That is why there might be a delay. Confirmations are an essential part of how the blockchain transfer works. You can find more information about Bitcoin confirmations in this Wiki article.
For altcoins, the arrival time depends on how long the transfer from your source wallet to ShapeShift would take (different cryptocurrencies may have different intervals). After ShapeShift receives and converts your altcoin to bitcoin, you will get the funds to your Wirex wallet in a few minutes. The entire process can take from a few minutes up to a few days.
If you used your local credit or debit card or Wirex card to purchase or exchange bitcoins, the funds should be reflected in your BTC balance instantly.