diff --git a/CHANGELOG.md b/CHANGELOG.md
index 590497f93b..adefb991de 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,10 @@
 
 ## Unreleased
 
+### Fixes
+
+- [#2342: Open fewer files at once during migration](https://github.com/alphagov/govuk-prototype-kit/pull/2342)
+
 ## 13.13.2
 
 ### Fixes
diff --git a/lib/utils/asyncSerialMap.spec.js b/lib/utils/asyncSerialMap.spec.js
new file mode 100644
index 0000000000..d665911a01
--- /dev/null
+++ b/lib/utils/asyncSerialMap.spec.js
@@ -0,0 +1,64 @@
+const { asyncSeriesMap } = require('./asyncSeriesMap')
+describe('asyncSerialMap', () => {
+  const nextTick = () => new Promise((resolve) => {
+    process.nextTick(() => resolve())
+  })
+
+  it('should work through an array and return the results', async () => {
+    const arr = ['abc', 'def', 'ghi']
+    const handler = async (item) => `"${item}"`
+
+    const result = await asyncSeriesMap(arr, handler)
+
+    expect(result).toEqual([
+      '"abc"',
+      '"def"',
+      '"ghi"'
+    ])
+  })
+
+  it('should work through an array and return the results', async () => {
+    const arr = ['abc', 'def', 'ghi']
+    const handler = async (item, index, array) => `"${item}|${index}|${JSON.stringify(array)}"`
+
+    const result = await asyncSeriesMap(arr, handler)
+
+    expect(result).toEqual([
+      '"abc|0|["abc","def","ghi"]"',
+      '"def|1|["abc","def","ghi"]"',
+      '"ghi|2|["abc","def","ghi"]"'
+    ])
+  })
+
+  it('should run these in series', async () => {
+    let latestResolve
+    let callCount = 0
+    const handler = (item) => new Promise((resolve, reject) => {
+      callCount++
+      latestResolve = resolve
+    })
+
+    const resultPromise = asyncSeriesMap(['abc', 'def', 'ghi'], handler)
+
+    await nextTick()
+
+    expect(callCount).toBe(1)
+    latestResolve('this is the first')
+
+    await nextTick()
+
+    expect(callCount).toBe(2)
+    latestResolve('this is the second')
+
+    await nextTick()
+
+    expect(callCount).toBe(3)
+    latestResolve('this is the third')
+
+    expect(await resultPromise).toEqual([
+      'this is the first',
+      'this is the second',
+      'this is the third'
+    ])
+  })
+})
diff --git a/lib/utils/asyncSeriesMap.js b/lib/utils/asyncSeriesMap.js
new file mode 100644
index 0000000000..0c3e7e879d
--- /dev/null
+++ b/lib/utils/asyncSeriesMap.js
@@ -0,0 +1,12 @@
+async function asyncSeriesMap (arr, handler) {
+  const results = []
+  let index = -1
+  while (arr.length > ++index) {
+    results.push(await handler(arr[index], index, arr))
+  }
+  return results
+}
+
+module.exports = {
+  asyncSeriesMap
+}
diff --git a/lib/utils/index.js b/lib/utils/index.js
index 594172d3ec..9830576e80 100644
--- a/lib/utils/index.js
+++ b/lib/utils/index.js
@@ -19,6 +19,7 @@ const plugins = require('../plugins/plugins')
 const routes = require('../routes/api')
 const { appDir, projectDir, packageDir } = require('./paths')
 const fse = require('fs-extra')
+const { asyncSeriesMap } = require('./asyncSeriesMap')
 
 // Tweak the Markdown renderer
 const defaultMarkedRenderer = marked.defaults.renderer || new marked.Renderer()
@@ -234,7 +235,7 @@ function recursiveDirectoryContentsSync (baseDir) {
 
 async function searchAndReplaceFiles (dir, searchText, replaceText, extensions) {
   const files = await fsp.readdir(dir)
-  const modifiedFiles = await Promise.all(files.map(async file => {
+  const modifiedFiles = await asyncSeriesMap(files, async file => {
     const filePath = path.join(dir, file)
     const fileStat = await fsp.stat(filePath)
 
@@ -248,7 +249,7 @@ async function searchAndReplaceFiles (dir, searchText, replaceText, extensions)
         return filePath
       }
     }
-  }))
+  })
 
   return modifiedFiles.flat().filter(Boolean)
 }
diff --git a/package.json b/package.json
index a620067940..1b1e059836 100644
--- a/package.json
+++ b/package.json
@@ -126,6 +126,6 @@
       "/node_modules/",
       "/tmp/"
     ],
-    "testTimeout": 30000
+    "testTimeout": 5000
   }
 }